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It has been recently proved that a variety of associative PI-superalgebras with graded involution of finite basic rank over a field of characteristic zero is minimal of fixed ⁎-graded exponent if, and only if, it is generated by a subalgebra of an upper block triangular matrix algebra, A : = U T Z 2 ⁎ ( A 1 , … , A m ) , equipped with a suitable elementary Z 2 -grading and graded involution. Here we give necessary and sufficient conditions so that Id Z 2 ⁎ ( A ) factorizes in the product of the ideals of ⁎-graded polynomial identities of its ⁎-graded simple components A i .

In the present paper it is proved that a variety of associative PI-superalgebras with graded involution of finite basic rank over a field of characteristic zero is minimal of fixed *-graded exponent if, and only if, it is generated by a subalgebra of an upper block triangular matrix algebra equipped with a suitable elementary ℤ2-grading and graded involution.

Let F be a field of odd characteristic and G a group. In 1991 Shalev established necessary and sufficient conditions so that the unit group of the group ring FG is metabelian when G is finite. Here, in the modular case, we do the same without restrictions on G. In particular, new cases emerge when G contains elements of infinite order.

In the 1980s Brian Hartley conjectured that if the unit group, \(\mathcal {U}(FG)\), of a torsion group ring FG satisfies a group identity, then FG satisfies a polynomial identity. The aim of this survey is to review the most relevant results that arose from the proof of this conjecture and discuss some recent developments and open questions concerning ∗-group identities for \(\mathcal {U}(FG)\) and group identities for the subgroup of its unitary units.

Let G be a nonabelian nilpotent group and F a field of characteristic p > 2, such that the unit group \(\mathcal {U}(FG)\) of the group ring FG is solvable and G contains a p-element. Here we provide a lower bound for the derived length of \(\mathcal {U}(FG)\) that corrects the result from Lee et al. (Algebr. Represent. Theory 17, 1597–1601 2014) when G is nontorsion and \(G^{\prime }\) is a finite p-group.

Actualmente la fotografía se encuentra en un proceso de reformulación constante que viene dado tanto por la acción que representa como por los espacios de participación donde se produce. Un proceso que incide directamente en la concepción del medio, en un ir y venir constante entre los aspectos clásicos de la imagen y la continua transformación de los entornos digitales. En su práctica artística contemporánea, la fotografía traspasa constantemente sus propias fronteras interactuando con otras disciplinas y desafiando la conceptualización de lo fotográfico. Ya no es posible la aproximación inocente al medio, la postfotografía ha dinamitado aún más sus límites para exigir una perpetua reflexión sobre el hecho fotográfico.

El fotoperiodismo contemporaneo no puede concebirse si no es desde la reflexion sobre sus objetivos, sus modos de produccion, sus formas de representacion, su difusion y su contextualizacion mediatica y social. En la actualidad, los fotografos no encuentran espacio en los medios de comunicacion donde publicar sus proyectos de largo alcance. En consecuencia, estan explorando nuevas vias para producir su trabajo y, entre las opciones posibles, hay dos que se han convertido en habituales: el crowdfunding y las becas que numerosas organizaciones no gubernamentales e instituciones ofrecen para ello. Ademas, la misma causa empuja a los autores hacia vias de publicacion y difusion propias de la esfera artistica —el foto-libro y la sala de exposiciones, entre otros—, propiciando asi un enriquecedor trasvase de estrategias creativas. Durante los ultimos diez anos, la organizacion sin animo de lucro The Aftermath Project ha llevado a cabo un concurso para apoyar proyectos fotograficos relacionados con las consecuencias de la guerra. Su finalidad es que dichos proyectos sirvan para mostrar el sufrimiento que queda detras del fin de los combates y, al mismo tiempo, contribuyan a reconstruir el danado tejido social. El presente trabajo es un estudio de caso que analiza el contenido de los 58 proyectos seleccionados desde 2006 a 2016 y tiene como objetivo ofrecer una perspectiva tematica y formal sobre la fotografia documental actual. Se analizan temas, ambitos geograficos y elecciones esteticas, partiendo de la hipotesis de que existe una convergencia cada vez mayor entre los modos de creacion de la fotografia documental y la artistica. Los resultados apuntan un sesgo euro-anglocentrico en las tematicas y geografias abordadas y, principalmente, numerosas tangencialidades creativas con la fotografia artistica contemporanea.

Given a minimal superalgebra A = A s s ⊕ J ( A ) , any subsequence of the graded simple summands of A s s determines a homogeneous subalgebra of A which is still a minimal superalgebra. In the present paper we provide a sufficient condition so that the T Z 2 -ideal of graded polynomial identities satisfied by A factorizes as the product of the T Z 2 -ideals associated to its suitable homogeneous subalgebras of such a type. We use this fact to show that in this event A generates a minimal supervariety of fixed superexponent.

Let FG be the group ring of a group G over a field F of characteristic different from 2, and let FG have an involution induced from one on G. Assuming that G has no elements of order 2 and no dihedral group involved, we determine the conditions under which the set of skew elements of FG is bounded Lie Engel. Furthermore, we make the determination with no restrictions upon G when the involution on FG is classical.

It has been shown that in characteristic zero the generators of the minimal supervarieties of finite basic rank belong to the class of minimal superalgebras introduced by Giambruno and Zaicev (Trans Am Math Soc 355:5091–5117, 2003). In the present paper the complete list of minimal supervarieties generated by minimal superalgebras whose maximal semisimple homogeneous subalgebra is the sum of three graded simple algebras is provided. As a consequence, we negatively answer the question of whether any minimal superalgebra generates a minimal supervariety.

Let F be a field of characteristic p > 2 and G a nonabelian nilpotent group containing elements of order p. Write F G for the group ring. The conditions under which the unit group 𝒰(F G) is solvable are known, but only a few results have been proved concerning its derived length. It has been established that if G is torsion, the minimum derived length is ⌈log2(p + 1)⌉, and this minimum occurs if and only if |G′| = p. In the present note, we show that the same holds if G has elements of infinite order.

SYNOPSISCurrent medical research on placebo effects has provided important new focus points for consideration by psychotherapists. Primary among these are the role of belief, meaning and context as key variables in successful placebo effects. This paper considers these findings in terms of what they may clarify, and challenge, regarding the critical variables necessary to beneficial therapeutic outcomes. combining these findings, it proposes the idea of the ‘therapy world’ as a pivotal common factor in determining the effectiveness of psychotherapeutic interventions

In the present paper we investigate minimal supervarieties of given superexponent over fields of characteristic zero. We show that any minimal supervariety of finite basic rank is generated by one of the minimal superalgebras, introduced by Giambruno and Zaicev in 2003. Furthermore it is proved that any minimal superalgebra, whose graded simple components of the semisimple part are simple, generates a minimal supervariety. Finally we state that the same conclusion holds when the semisimple part of a minimal superalgebra has exactly two arbitrary graded simple components.

Let A be a non-trivial semiprime associative superalgebra with superinvolution. In the present note we investigate when the subspaces of symmetric elements or skew elements of A are Lie nilpotent or Lie solvable. We show that these conditions determine the algebraic structure of A. © 2012 Elsevier Inc.

Let F be an infinite field of characteristic different from 2 and G a torsion group. Write 𝒰+(FG) for the set of units in the group ring FG that are symmetric with respect to the classical involution induced from the map g ↦ g −1, for all g ∈ G. We classify the groups such that ⟨𝒰+(FG)⟩ is n-Engel.

In Di Vincenzo and La Scala (2007) [1] , given a n-tuple ( A 1 , … , A n ) of finite dimensional *-simple algebras over a field of characteristic zero, a block-triangular matrix algebra with involution, denoted by R : = UT * ( A 1 , … , A n ) , was introduced and it was proved that any finite dimensional algebra with involution which is minimal with respect to its *-exponent is *-PI equivalent to R for a suitable choice of the algebras A i . Motivated by a conjecture stated in the same paper, here we show that R is *-minimal when either it is *-symmetric or n = 2 .

Let F be a field of characteristic different from 2, and G a group with involution ∗ . Write ( F G ) + for the set of elements in the group ring F G that are symmetric with respect to the induced involution. Recently, Giambruno, Polcino Milies and Sehgal showed that if G has no 2-elements, and ( F G ) + is Lie nilpotent (resp. Lie n -Engel), then F G is Lie nilpotent (resp. Lie m -Engel, for some m ). Here, we classify the groups containing 2-elements such that ( F G ) + is Lie nilpotent or Lie n -Engel.

This paper considers critically the major similarities and differences between coaching and therapy as presented by previous authors. In particular, it considers Jopling’s contribution of the idea of a ‘fuzzy space’ between the professions and argues that coaching psychology is particularly well placed to inhabit this ‘fuzzy space’. Finally, the paper considers three major issues that provide pathways to both convergence and divergence between the professions: contracting; the quality and type of relationship being engendered; and the inter-relational stance.

This paper explores the issue of conflict within the coaching context from an existential perspective. It introduces the idea of existence tensions as a means to address and expose the polar aspects of conflict from which existential theory takes its position regarding the inevitability of conflict in human experience. The paper also distinguishes two types of conflict: dissonant and consonant conflict and addresses the importance of. coaches’ awareness of their differences in order to enhance the quality and effectiveness of their interventions. Finally, the paper summarises a number of key arguments regarding conflict developed by Jean-Paul Sartre and contextualises these within the profession of coaching.

Let KG be a non-commutative strongly Lie solvable group algebra of a group G over a field K of positive characteristic p. In this note we state necessary and sufficient conditions so that the strong Lie derived length of KG assumes its minimal value, namely [log2(p + 1)].

Giambruno and Zaicev (Trans Am Math Soc 355:5091–5117, 2003) characterized varieties of associative PI-algebras over a field of characteristic zero which are minimal of fixed exponent. The aim of the present survey paper is to discuss this result and the recent developments on the corresponding problem for PI-algebras endowed with a $$\mathbb {Z}_2$$ -grading. In particular, we provide an example of minimal superalgebra not generating a minimal supervariety of fixed superexponent, thereby partially answering the question of which actually are the generators of minimal supervarieties of finite basic rank.

This paper explores the experience of change in psychotherapy from an existential perspective. It proposes three variants of change experience, of which the third, those change experiences that are reflectively troubling and deemed to be destructive, undesirable, and debilitating, is particularly pertinent to psychotherapeutic practice. Further, the paper explores various existentially-derived paradoxes and polarities associated with the experience of change and considers what factors may be involved that shift our relationship to change from that of being unwanted and threatening towards that of a reflective willingness ‘to meet’ change experiences and engage with their existential possibilities.

In this article we introduce the series of the upper Lie codimension subgroups of a group algebra KG of a group G over a field K. By means of this series we give a contribution to the conjecture cl L (KG) = cl L (KG) when G belongs to particular classes of finite p-groups.

Existential psychotherapy places pivotal significance upon the inter-relational aspects of human experience. By so doing, the therapeutic relationship itself becomes the principal means through which the client’s presenting symptoms and disorders are disclosed as direct expressions and outcomes of the client’s overall “way of being” rather than as isolated and disruptive impediments. At the same time, existential therapy emphasises the actual relationship that emerges between psychotherapist and client and argues that it is via the contrast and comparison of this lived experience with that of their ‘wider world’ experience that clients can find the means to reconsider and reconstruct their “ways of being”. This paper seeks to demonstrate that, as well as their shared aims and methods of enquiry, it is the mutual emphasis upon inter-relatedness as a foundational value for human enquiry that reveals substantive and intriguing points of connection between existential psychotherapy and phenomenological enquiry. The paper furthermore argues that existential psychotherapy might best be viewed as a clearly formulated expression of phenomenological enquiry.

Let \(K\) be a field of positive characteristic \(p\) and \(KG\) the group algebra of a group \(G\). It is known that, if \(KG\) is Lie nilpotent, then its upper (and lower) Lie nilpotency index is at most \(|G^{\, \prime}|+1\), where \(|G^{\, \prime}|\) is the order of the commutator subgroup. The authors previously determined those groups \(G\) for which this index is maximal and here they determine the groups \(G\) for which it is `almost maximal', that is, it takes the next highest possible value, namely \(|G^{\, \prime}|-p+2\).

For a restricted Lie algebra L over a field of characteristic p > 0 we study the Lie nilpotency index t L (u(L)) of its restricted universal enveloping algebra u(L). In particular, we determine an upper and a lower bound for t L (u(L)). Finally, under the assumption that L is p-nilpotent and finite-dimensional, we establish when the Lie nilpotency index of u(L) is maximal. Communicated by I. Shestakov.

We characterize the restricted Lie algebras L whose restricted universal enveloping algebra u(L) is Lie metabelian. Moreover, we show that the last condition is equivalent to being u(L) strongly Lie metabelian.

In the present paper we give the full description of the Lie nilpotent group algebras which have maximal Lie nilpotency indices.

Let L be a non-abelian restricted Lie algebra over a field of characteristic p > 0 and let u(L) denote its restricted enveloping algebra. In Siciliano (Publ Math (Debr) 68:503–513, 2006) it was proved that if u(L) is Lie solvable then the Lie derived length of u(L) is at least ⌈log2(p + 1)⌉. In the present paper we characterize the restricted enveloping algebras whose Lie derived length coincides with this lower bound.

In this paper we prove some results about the derived length of the unit group of a group algebra. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Let G be a nonabelian free group with involution *. In the present note, we show that G satisfies a *-group identity if and only if * is the classical involution, given by \({g^\ast=g^{-1}}\) for all \({g \in G}\).

Existential psychotherapy places pivotal significance upon the interrelational aspects of human experience. By so doing, the therapeutic relationship itself becomes the principal means through which the client's presenting symptoms and disorders are disclosed as direct expressions and outcomes of the client's overall “way of being” rather than as isolated and disruptive impediments. This paper examines the therapeutic relationship as viewed from four primary interrelational dimensions. Further, it focuses upon psychotherapy's tendency to exclude “the world” from the therapeutic relationship and provides two novel and challenging alternatives whose principal aim is to “bring the world back into the therapeutic relationship.”

Although therapeutic thinking and practice have entered their second century, most practitioners remain largely uncertain as to what data to trust, including "what works" and, "why it works." If anything, practitioners' reliance on ever-increasing numbers of theoretical models and either vague or contradictory research findings as primary guidelines to their practice has added to the confusion. What can the practitioner trust? This paper puts forward the "dangerous proposal" that it is of primary value for clinical professionals to place their trust on an often overlooked variable: the clients' statements about their therapy and their relationship to and with their therapist. It is argued that through the clarification of this variable will emerge a better understanding of the nonspecific variables of the therapeutic relationship itself and, as significantly, of the encompassing interrelational realms of discourse evident in all therapeutic models. OUTCOME VARIABLES: PSYCHOTHERAPISTS' ASSUMPTIONS In a recent article by Scott Miller, various significant quandaries regarding psychotherapists' assumptions about significant outcome variables were brought out (1). Among these were the following: 1. The most successful treatments of depression were those that employed psychotherapeutic interventions alone. Indeed, it has been argued that "[m]ore effective therapists have a psychological rather than biological orientation in their treatment approach" (Blatt et al., quoted in 1, p. 40). 2. Combined treatments employing medication and psychotherapy were less effective than those treatments that only employed psychotherapy (Beutler, in [1]). 3. While 96% of studies funded by drug companies showed favorable results for the treatment of various psychological disorders via medication, only 37 % of studies not funded by drug companies showed similar results (1). Miller concluded that "[o]ver the decades, generations of therapists have come to suspect that it isn't so much what they do-what theory, what model, what technique or even what medication-that helps people, but who they are and who their clients are, as well as the idiosyncratic personal fit between themselves and the people who come to see them" (1, p. 40). OUTCOME VARIBLES: CLIENTS' STATEMENTS In line with this conclusion, numerous studies have indicated "that the quality and strength of the therapeutic relationship was the primary determinant of successful outcome across treatments-including medication" (1, p. 41). But what is it about the therapeutic alliance itself that might determine what are the significant variables that will increase the likelihood of positive outcomes? In their important text, Handbook of Psychotherapy Integration, Norcross and Goldfried emphasized various qualitative factors that are common to the major therapies as being far more significant than any specific factors that have been identified with any particular model or theory of psychotherapy (2). Of most interest to this discussion are those studies that focused upon clients' statements concerning the effectiveness of treatment. Clients most frequently attribute successful treatment outcomes to the personal qualities of their therapist. Specifically, the therapist's ability and willingness to understand and accept them emerge as the most significant variables across numerous studies (2). David Howe's invaluable text, On Being a Client, confirms the above conclusion (3). Further, Howe lists three key factors in clients' perspectives regarding what they found to be necessary factors for the success of their therapy. The first, and by far the most widespread, response emphasized the clients' experience of having the opportunity to talk in a structured setting. The fact that clients could sit in a room and talk for a particular period of time was perceived by them as being by far the most valuable and beneficial therapeutic variable. …

Until recently, perhaps the major avenues of working with severely disturbed patients have been based upon either organic-chemical or intrapsychic determinants and treatment components. One recent development is an emphasis upon interpsychic and interpersonal factors and determinants in both the understanding and the treatment of extreme psychotic disturbances. Existential, systemic, and cognitive-behavioral conceptualizations and therapies maintain substantial independence of one another. Yet these three share at least two significant commonalities. One is that they each emphasise the interpsychic and interpersonal. A second is this first commonality has led to some exciting new developments in the understanding and treatment of psychosis.

This paper expresses the author's personal view on the question of evil as considered by psychotherapeutic theories. It challenges the psychotherapeutic tendency to avoid the moral and existential dimensions of evil via the transformative language of psychopathology which allows theorists and practitioners either implicitly or explicitly to rely upon metaphors of disease or immaturity-be it physical or psychic. The author argues that such views are problematic not least because they mimic the separatist attitudes of those persons who have been labelled as evil since both rely upon notions of being 'less than fully human'. Further, taking a perspective that is informed by existential-phenomenological theory, the author highlights the inconsistencies and limitations that arise when the issues surrounding evil are considered from an intrapsychic perspective. As an alternative to this dominant tendency within psychotherapy and psychology, the author presents an inter-psychic viewpoint derived, in part, from t...

Let F be a field of characteristic p ≠ 2 and G a group without 2-elements having an involution ∗. Extend the involution linearly to the group ring FG, and let (FG)− denote the set of skew elements with respect to ∗. In this paper, we show that if G is finite and (FG)− is Lie metabelian, then G is nilpotent. Based on this result, we deduce that if G is torsion, p > 7 and (FG)− is Lie metabelian, then G must be abelian. Exceptions are constructed for smaller values of p.

Let F be a field of characteristic p ≠ 2 and G a group without 2-elements having an involution *. Write ( F G ) + $(FG)^+$ for the set of elements in the group ring F G that are symmetric with respect to the induced involution. In the present note, we show that if G is finite and ( F G ) + $(FG)^+$ is Lie metabelian, then G is nilpotent. Based on this result, we deduce that if G is torsion, p ≠ 3 and ( F G ) + $(FG)^+$ is Lie metabelian, then G must be abelian. This extends a result of Levin and Rosenberger.

Let F be a field of characteristic different from 2 and G a group. Under the classical involution on the group ring FG , we show that if FG is modular, then the group of unitary units of FG is nilpotent if and only if the entire unit group is nilpotent. We also demonstrate that this does not necessarily hold if FG is not modular, but it is still true if F is algebraically closed.

Let G be an arbitrary abelian group. In the present paper we study the question of whether G-graded upper block triangular matrix algebras over a field of characteristic zero are determined, up to G-graded isomorphism, by their G-graded polynomial identities. We obtain some results for an elementary grading and, as a consequence, for any grading over an algebraically closed field.

The hypothesis of transference has become such a fundamental assumption for many therapeutic practitioners, that it is rarely questioned either in terms of its theoretical value or its function. This paper will critically examine the notion of transference from an existential‐phenomenological perspective and will argue the case for an alternative perspective. Further, it will seek to demonstrate that numerous and significant logical and applied problems arise with regard to the hypothesis of transference—problems which have a major negative impact upon the therapeutic relationship in general and upon the possibility of ‘encounter‘—or ‘meeting‘—between therapist and client. Finally, the paper will seek to show how, in many cases, the adoption of the hypothesis of transference can be seen as a defensive and power‐preserving (or enhancing) activity on the part of the therapist whose benefit to the client is, at best, questionable.

Let F be a field of characteristic different from 2 and G a group with involution ∗ . Extend the involution to the group ring F G , and write ( F G ) − for the Lie subalgebra of F G consisting of the skew elements. We classify the torsion groups G having no elements of order 2 such that ( F G ) − is bounded Lie Engel.