Let Int be the lattice of all intervals of an -algebra . In the present paper we investigate the relations between direct product decompositions of and (i) the lattice Int , or (ii) 2-periodic isometries on , respectively.
Among completely regular locales, we characterize those that have the feature described in the title. They are, of course, localic analogues of what are called -isocompact spaces. They have been considered in T. Dube, I. Naidoo, C. N. Ncube (2014), so here we give new characterizations that do not appear in this reference.
Let be the ring of real-valued continuous functions on a frame . The aim of this paper is to study the relation between minimality of ideals of and the set of all zero sets in determined by elements of . To do this, the concepts of coz-disjointness, coz-spatiality and coz-density are introduced. In the case of a coz-dense frame , it is proved that the -ring is isomorphic to the -ring of all real continuous functions on the topological space . Finally, a one-one correspondence is...
We study the minimal prime elements of multiplication lattice module over a -lattice . Moreover, we topologize the spectrum of minimal prime elements of and study several properties of it. The compactness of is characterized in several ways. Also, we investigate the interplay between the topological properties of and algebraic properties of .
n×m-valued Łukasiewicz algebras with negation were introduced and investigated in [20, 22, 23]. These algebras constitute a non trivial generalization of n-valued Łukasiewicz-Moisil algebras and in what follows, we shall call them n×m-valued Łukasiewicz-Moisil algebras (or LM n×m -algebras). In this paper, the study of this new class of algebras is continued. More precisely, a topological duality for these algebras is described and a characterization of LM n×m -congruences in terms of special subsets...
This paper deals with a new interpretation of a special functional characterisation of Sheffer strokes, with the study of morphisms and the construction of different De Morgan Algebras on a given set.
In this paper we apply the notion of the product -algebra in accordance with the definition given by B. Riečan. We investigate the convex embeddability of an -algebra into a product -algebra. We found sufficient conditions under which any two direct product decompositions of a product -algebra have isomorphic refinements.