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An explicit categorical equivalence is defined between a proper subvariety of the class of $PMV$-algebras, as defined by Di Nola and Dvure$\check{c}$enskij, to be called $PMV_f$-algebras, and the category of semi-low $f_u$-rings. This categorical representation is done using the prime spectrum of the $MV$-algebras, through the equivalence between $MV$-algebras and $l_u$-groups established by Mundici, from the perspective of the Dubuc-Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low $f_u$-rings associated to Boolean algebras are characterized. Besides we show that class of $PMV_f$-algebras is coextensive.

In this article we develop a new version of the intuitionist existential graphs presented by Arnol Oostra [4]. The deductive rules presented in this article have the same meaning as those described in the work of Yuri Poveda [5], because the deductions according to the parity of the cuts are eliminated and are replaced by a finite set of recursive rules. This way, $ Alfa_I $ the existential graphs system for intuitional propositional logic follows the course of the deductive rules of the system $ Alfa_0 $ described by Poveda [5], and is equivalent to the intuitionistic propositional calculus. In this representation the $ Alfa_0 $ system is improved, there are a series of deductive rules of second degree incorporated that previously had not been considered and that allow a better management of deductions and finally from the ideas proposed by Van Dalen [6], a mixture is incorporated in the deduction techniques, the natural deductions of the Gentzen system are combined with new system rules $ Alfa_0 $ and $ Alfa_I $. The symbols proposed for the $Alfa_I$ representation relate open, closed and quasi-open sets of the usual topology of the plot with the intuitional propositional logic, usefull for approaching new problems in the representation of this logic from a more geometrical perspective.

In this paper, a new algebraic structure is defined, which is a new MV-algebra that has a product operation, we will call it MVW-rig (Multivalued-weak rig). This structure is defined with universal algebra axioms, it is presented with a good amount of natural examples in the MV-algebra environment and the first results having to do with ideal, quotients, homomorphisms and subdirect product are established. In particular, its prime spectrum is studied, that with the co-Zariski topology it is compact. Consequently, a good number of results that are analogous to the theory of commutative rings and rigs are presented with which this theory keeps a close relationship to., Comment: in English

In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem., 1 and 1/2 pages

En este trabajo de investigación, se establece de manera explícita la equivalencia categórica entre una subvariedad propia de la clase de PMV -álgebras que llamaremos PMVf -álgebras (PMV -álgebras de funciones), y la categoría de los fu-anillos semi-low. Esta representación categórica se realiza con el espectro primo de las MV -álgebras, a través de la equivalencia entre MV -álgebras y lu-grupos establecida por Mundici, pero desde la perspectiva de Dubuc-Poveda, que extiende la construcción definida por Chang para cadenas. Como caso particular, se caracterizan los fu-anillos asociados por esta equivalencia a las álgebras de Boole. Se estudian algunos anillos de funciones continuas a trozos de [0, 1] en [0, 1] cuyos componentes están constituidos por un número finito de polinomios con coeficientes enteros. Estos casos de ¿curvas algebraicas¿ (curvas tratadas como ceros de los polinomios que la componen), corresponden a una subclase de PMVf-álgebras relacionadas con las PMVf-álgebras libres de la variedad generada por el intervalo [0, 1], HSP[0, 1]. Por último, dado que la categoría de f-anillos con unidad fuerte contiene una clase de anillos no unitarios, como por ejemplo algunos ideales principales en el anillo de funciones continuas con valores en un espacio topoló-gico compacto, probamos así la co-extensividad de una categoría esencialmente diferente a la categoría de anillos conmutativos unitarios. Como consecuencia, obtenemos la co-extensividad de algunas subcategorías plenas de las MV -álgebras con producto, a través de la equivalencia entre las PMVf-álgebras y los fu-anillos Doctorado DOCTOR(A) EN CIENCIAS - MATEMÁTICAS