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We give a simple approach to determine when multiplication is associative for matrices of infinite size, extending recent results of Bossaller and Lopez-Permouth.

People tend to better remember same-race faces relative to other-race faces (an "own-race" bias). We examined whether the own-race bias extends to associative memory, particularly in the identification and recall of information paired with faces. In Experiment 1, we presented white participants with own- and other-race faces which either appeared alone or accompanied by a label indicating whether the face was a "criminal" or a "victim". Results revealed an own-race facial recognition advantage regardless of the presence of associative information. In Experiment 2, we again paired same- and other-race faces with either "criminal" or "victim" labels, but rather than a recognition test, participants were asked to identify whether each face had been presented as a criminal or a victim. White criminals were better categorised than Black criminals, but race did not influence the categorisation of victims. In Experiment 3, white participants were presented with same- and other-race faces and asked to remember where the person was from, their occupation, and a crime they committed. Results revealed a recall advantage for the associative information paired with same-race faces. Collectively, these findings suggest that the own-race bias extends to the categorisation and recall of information in associative memory.

A dendriform algebra is an associative algebra whose product splits into two binary operations and the associativity splits into three new identities. These algebras arise naturally from some combi...

Cued recall of word pairs is improved by asking participants to combine items in an interactive image. Meanwhile, interactive images facilitate serial-recall (Link Method), but even better when each item is imagined alongside a previously learned peg-word (Peg List Method). We asked if a peg system could support memory for pairs, hypothesising it would outperform interactive imagery. Tested with cued recall, five study strategies were manipulated between-subjects, across two experiments: (1) Both words linked to one peg; (2) Each word linked to a different peg; (3) Peg list method but studying as a serial list; (4) Interactive imagery (within-pairs); (5) Link Method. Participants were able to apply peg-list strategies to pairs, as anticipated by mathematical modelling. Error-patterns spoke to mathematical models; peg lists exhibited distance-based confusability, characteristic of positional-coding models, and errors tended to preserve within-pair position, even for inter-item associative strategies, suggesting models of association should incorporate position. However, the peg list strategies came with a speed-accuracy tradeoff and did not challenge the superiority of the interactive imagery strategy. Without extensive practice with peg list strategies, interactive imagery remains superior for associations. Peg strategies may excel instead in tasks that primarily test serial order or with extensive training.

We describe the groups of automorphisms of two generated free braided associative algebras with involutive diagonal braidings over a field of characteristic $\neq 2$. Depending on the form of the diagonal involutive braiding, five different automorphism groups arise as automorphism groups of two generated free braided associative algebras. This list covers all three automorphism groups that arise in the case of quantum planes \cite{AC}., 14 pages

In this paper, an impulsive Cohen-Grossberg bidirectional associative neural network with both time-varying and distributed delays is examined. Novel sufficient conditions for deriving stability wi...

Temporal and semantic associative processes during the acquisition of new verbal information undergo various changes across the life span. Temporal order clusters and subjective clusters were monitored during verbal learning trials using the Rey (Auditory Verbal Learning Task) for 1471 participants aged 8-91. Pairs, three-word, and four-word clusters were measured. Subjective clusters were generated at similar frequency across the whole life span. By contrast, a clear inverted-U curve across life span was indicated for temporal clusters. More words were subjectively clustered than clustered by temporal presentation order. The number of words clustered increased across trials, and cluster types showed a different increase profile across trials. The subjective cluster increment was faster and steeper than the temporal cluster increment in most of the age segments. Life span trajectory tendencies in the formation of temporal and semantic associations in recall were interpreted in relation to different frameworks of cognitive life span changes.

In this article, we classify the irreducible integrable modules for the loop affine-Virasoro algebra ((g°⊗C[t,t−1]⊕CK)⋊ Vir)⊗A, where A is a finitely generated commutative associative unital algebr...

Factor systems are a tool for working on the extension problem of algebraic structures such as groups, Lie algebras, and associative algebras. Their applications are numerous and well-known in these common settings. We construct $\mathscr{P}$ algebra analogues to a series of results from W. R. Scott's $\textit{Group Theory}$, which gives an explicit theory of factor systems for the group case. Here $\mathscr{P}$ ranges over Leibniz, Zinbiel, diassociative, and dendriform algebras, which we dub "the algebras of Loday," as well as over Lie, associative, and commutative algebras. Fixing a pair of $\mathscr{P}$ algebras, we develop a correspondence between factor systems and extensions. This correspondence is strengthened by the fact that equivalence classes of factor systems correspond to those of extensions. Under this correspondence, central extensions give rise to 2-cocycles while split extensions give rise to (nonabelian) 2-coboundaries., Comment: 22 pages

This paper is devoted to the study of four-dimensional commutative power-associative non-Jordan train algebras. The existence of a unique orthogonal idempotent element in such kind of algebras enab...

Aging impairs visual associative memories. Up to date, little is known about whether aging impairs auditory associative memories. Using the head-related-transfer function to induce perceived spatial locations of auditory phonemes, this study used an audiospatial paired-associates-learning (PAL) paradigm to assess the auditory associative memory for phoneme-location pairs in both younger and older adults. Both aging groups completed the PAL task with various levels of difficulty, which were defined by the number of items to be remembered. The results showed that compared with younger participants' performance, older participants passed fewer stages and had lower capacity of auditory associative memory. For maintaining a single audiospatial pair, no significant behavioral differences between the two aging grous werefound. However, when multiple sound-location pairs were required to be remembered, older adults made more errors and demonstrated a lower working memory capacity than younger adults. Our study indicates aging impairs audiospatial associative learning and memory.

Weakly associative algebras are a class of Lie-admissible algebras that generalize associative algebras and useful to extend the class of formal deformations of associative commutative algebras. Th...

Let R be an associative and commutative ring with unity 1 and consider k∈N such that 1+1+⋯+1=k is invertible. Let UT∞(k)(R) be the group of upper triangular infinite matrices whose diagonal entries...

In this paper we give an in-deph analysis of the nilpotency index of nilpotent homogeneous inner superderivations in associative prime superalgebras with and without superinvolution. We also presen...

According to the associative deficit hypothesis, older adults experience greater difficulty in remembering associations between pieces of information than young adults, despite their relatively intact memory for individual items. It has been demonstrated that this deficit could be simulated by depleting resources for relational processing. The current study examines the possible mechanisms underlying this simulation. Item and associative memory were assessed using a process dissociation paradigm in which word pairs were encoded under full attention (FA) or relational divided attention (DA) conditions across three groups: FA older adults (

We describe the universal associative enveloping algebra of a Lie–Jordan algebra with a unit over a field of characteristic 0. We show that if L is a Lie–Jordan algebra with a unit e over a field F...

The ability to generate associative representations and to retrieve them from long-term episodic memory generally declines in healthy aging. However, it is unclear whether healthy aging has differential effects on associative memory for identity, spatial configuration, and temporal order relationships. In the current study, we assessed how healthy aging impacts on associative memory for identity, spatial, or temporal relationships between pairs of visual objects via discrimination of intact and rearranged pairs. Accuracy and response time performance of healthy older adults (aged 65-80) were compared with young adults (ages 19-30). Age-related declines in associative memory were observed equally for all types of associations, but these declines differed by associative status: aging most strongly affected ability to discriminate rearranged pairs. These results suggest that associative memory for identity, spatial, and temporal relationships are equally affected by healthy aging, and may all depend on a shared set of basic associative mechanisms.

Let S and R be two associative rings, SCR be a faithfully balanced (S, R)-bimodule. We introduce and investigate properties of ∞-torsionfree modules with respect to SCR, which are generalizations o...

Given elements a, b, c of any associative ring R with 1, then a is called right hybrid (b, c)-invertible if there exists y∈R such that yay=y,yR=bR and rann(y)=rann(c). It is shown that such y exist...

Humanist and political conceptions of human rights disagree about whether human rights are best conceived as either general or associative rights. According to humanist conceptions human rights are...

First we prove that any inner automorphism in the stabilizer of a graded-simple unital associative algebra whose grading group is abelian is the conjugation by a homogeneous element. Now consider a grading by an abelian group on an associative algebra such that the algebra is graded-simple and satisfies the DCC on graded left ideals. We give necessary and sufficient conditions for the grading to be fine. Then we assume that one of these necessary conditions to be fine is satisfied, and we compute the automorphism groups of the grading; the results are expressed in terms of the automorphism groups of a graded-division algebra. Finally we compute the automorphism groups of graded-division algebras in the case in which the ground field is the field of real numbers, and the underlying algebra (disregarding the grading) is simple and of finite dimension., Comment: 15 pages

In this paper we give the classification of 5-dimensional complex nilpotent associative algebras. We use χ ( A ) = ( dim A , dim A 2 , dim A 3 , … , dim A n ) - the isomorphism invariant. We prove ...

Research has independently highlighted the roles of semantic memory and associative abilities in creative thinking. However, it remains unclear how these two capacities relate to each other, nor ho...

We give an intriguing construction for establishing a sequence of unital, commutative, associative number systems by introducing the Z 2 -graded algebra S L n ( R ) . We show how the algebra S L n ...

In this article, we study homotopes of finite-dimensional algebras (not necessarily, associative). In the case of associative algebras, we study homotopes by the methods of Category theory and give...

We present an eight-dimensional even sub-algebra of the 2^4 = 16-dimensional associative Clifford algebra Cl(4,0) and show that its eight-dimensional elements denoted as X and Y respect the norm relation ||XY|| = ||X|| ||Y||, thus forming an octonion-like but associative normed division algebra, where the norms are calculated using the fundamental geometric product instead of the usual scalar product so that the underlying coefficient algebra resembles that of split complex numbers instead of reals. The corresponding 7-sphere has a topology that differs from that of octonionic 7-sphere.

This paper is concerned with the algebraic and geometric classification of the commutative power-associative algebras of dimension ≤4 over an algebraically closed field k with characteristic relati...

After the Second World War, the dominant thinking in France was linked to a desire for solidarity. In this context, there was a real desire to develop an offer of education for all. Many associatio...

In this paper, we provide the complete characterization of integer sequences that are characteristic sequences for general non-associative algebras, i.e., we determine the set of combinatorial prop...

The Gelfand-Kirillov dimension measures the asymptotic rate of growth of algebras. For every associative dialgebra D, the quotient AD:=D/Id(S), where Id(S) is the ideal of D generated by the set S:...

The Mushroom Body (MB) is the primary location of stored associative memories in the Drosophila brain. We discuss recent advances in understanding the MB's neuronal circuits made using advanced light microscopic methods and cell-type-specific genetic tools. We also review how the compartmentalized nature of the MB's organization allows this brain area to form and store memories with widely different dynamics.

In this article, we consider the category of unitary right modules over an (associative) ring and the category of firm right modules over an idempotent ring. We study monomorphisms in these categor...

Older people are more prone to memory distortions and errors than young people, but do not always show greater false recognition in the Deese-Roediger-McDermott (DRM) task. We report two preregistered experiments investigating whether recent findings of age-invariant false recognition extend to designs in which studied items are blocked. According to Tun, Wingfield, Rosen, & Blanchard (1998), age effects on false recognition in the DRM task are due to a greater reliance on gist processing which is enhanced under blocked study conditions. Experiment 1 assessed false recognition in an online variant of the DRM task where words were presented visually, with incidental encoding. The results showed Bayesian evidence against greater false recognition by older adults, whether lures were semantically associated with studied lists, or perceptually related (presented in the same distinctive font as studied lists) or both. Experiment 2 used a typical DRM procedure with auditory lists and intentional encoding, closely reproducing Tun et al.’s (1998) Experiment 2 but omitting an initial test of recall. The results showed evidence against an age-related increase in critical lure false recognition under these conditions. Together, the data suggest that older people do not make more associative memory errors in recognition tests than young people.

In this paper, we consider non-associative generalisations of Hajek's logics BL and psBL. As it was shown by Cignoli, Esteva, Godo, and Torrens, the former is the logic of continuous t-norms and th...

Let F denote a field with char F=2. The Racah algebra R is the unital associative F-algebra defined by generators and relations in the following way. The generators are A, B, C, D. The relations as...

Individual creativity support systems (ICSSs) increase idea generation by providing external stimuli, such as relevant words. However, it is not clear how different elements of ICSS design affect h...

This study examines how sampled Chinese and U.S. third and fourth grade students (NChina = 167, NUS = 97) understand the commutative, associative, and distributive properties. These students took b...

We investigated the extent to which activation of specific information in associative networks during a memory task could facilitate subsequent analogical problem solving in healthy older adults as well as those with early onset Alzheimer’s disease. We also examined whether these priming effects were stronger when the activation of the critical solution term during the memory task occurred when the item was actually presented (true memories) or when this item arose due to spreading activation to a related but nonpresented item (false memory). Older adult controls (OACs) and people with Alzheimer’s disease (AD) were asked to solve 9 verbal proportional analogies, 3 of which had been primed by Deese/Roediger-McDermott lists where the critical lure (and problem solution) was presented as a word in the list (true memory), 3 of which were primed by DRM lists whose critical lures were spontaneously activated during list presentation (false memory), and 3 of which were unprimed. As expected, OACs were better (both in terms of speed and accuracy) at solving problems than people with AD and both groups were better when false memories were primes than when true memories were primes or there were no primes. There were no reliable differences between unprimed and true prime problems. These findings demonstrate that (a) priming of problem solutions extends to verbal proportional analogies in OACs and people with AD, (b) false memories are more effective at priming problem solutions than true memories, and (c) there are clear positive consequences to the production of false memories.

Moran and Bar-Anan (Moran, T., & Bar-Anan, Y. (2013). The effect of object-valence relations on automatic evaluation. Cognition and Emotion, 27(4), 743–752) demonstrated that evaluations on a direct measure reflected information on both US valence and CS-US relations, whereas evaluations on an indirect measure (IAT) reflected only information on US valence. This dissociation between measures supposedly tapping into propositional and associative processes apparently supports dual process models of EC. In the present study, we present an alternative explanation of this pattern, based on an interpretation of IAT effects in terms of flexible similarity construction processes. According to this account, processing draws on those features that discriminate between target categories, and help to align targets with attributes in the compatible block. Across two experiments, we consistently found that IAT effects did not reflect rigid associations, but instead depended on whichever information could be used for similarity constructions between targets and attributes in different variants of the IAT. The findings are discussed with regard to theoretical models of EC as well as in reference to prominent accounts of IAT performance.

Let R be an associative ring with identity 1. We describe all idempotent matrices with only zeros and ones on the diagonal in T(n,R) – the ring of n×n upper triangular matrices over R (n∈N), and T(...

In this paper, we investigate the existence and representations of the generalized inverse AT,∗(2), AT,∗(1,2), A∗,S(2), A∗,S(1,2), AT,S(2), AT,S(1,2) of a matrix A over an associative ring, and giv...

In order to construct a class of new Turaev-braided group category with nontrivial associativity, the concept of a quasitriangular quasi-Turaev group coalgebras was recently introduced. Inside the ...

In this article, we study third power associative, antiflexible rings satisfying the identity (a,b,bc)=b(a,b,c). We prove that third power associative, antiflexible rings satisfying the identity (a,b,bc)=b(a,b,c) with characteristic ≠2,3 are associative of degree five. As a consequence of this result, we prove that a third power associative semiprime antiflexible ring satisfying the identity (a,b,bc)=b(a,b,c) is associative.

In many research literatures, the dynamical behaviour of cellular neural networks (CNNs) is simplified by using cloning template. However, the flaws of cloning template are obvious, because the cor...

How do racial signals associating a candidate with minority supporters change voters’ perceptions about a candidate and their support for a candidate? Given the presence of competing information in any campaign or the absence of information in low-salience campaigns, voters may rely on heuristics–such as race–to make the process of voting easier. The information communicated by these signals may be so strong that they cause voters to ignore other, perhaps more politically relevant, information. In this paper, we test how associative racial cues sway voters’ perceptions of and support for candidates using two experiments that harness real-world print and audio campaign advertisements. We find that the signals in these ads can sometimes overwhelm cues about policy positions when the two are present together. Moreover, we find that such signals have limited effects on candidate support among Black voters but that they risk substantial backlash of up to eight percentage points in reported vote intention among White voters. Our results highlight how voters gather and use information in low-information elections and demonstrate the power of campaign communication strategies that use racial associations.

Recent work has suggested that issue ownership has a competence and an associative dimension and that both dimensions are less stable than originally assumed. This study is the first attempt to directly compare the stability and change of voters’ perceptions on both dimensions. Using data from the 2015 Swiss Election Study, linking data from a combined panel/rolling cross-section survey with an extensive media analysis, this study finds that voters are more likely to maintain their issue ownership perceptions if the party they identify as the issue owner before the campaign receives a higher share of media campaign coverage. This stabilizing effect is conditional on the importance of the issue for the voter, and it is stronger for voters’ competence evaluations than for their party-issue associations, which proved to be more stable. Thus, the results confirm the literature’s previously untested assumption that voters’ associative ownership perceptions are more stable than their competence ownership evaluations.

The present study investigated the children’s capabilities of utilizing analytic strategies in Chinese character learning using an associative pseudocharacter learning paradigm. The participants we...

In this note, the authors introduce the notion of soft sets (briefly, S-sets) in an ordered AG-groupoid. We define and give some examples of SI-l-ideals, SI-r-ideals, and SI -bi-ideals in an ordere...