Ideals, -rings and -algebras
Ideals of noncommutative -monoids
In this paper, we introduce the concept of an ideal of a noncommutative dually residuated lattice ordered monoid and we show that congruence relations and certain ideals are in a one-to-one correspondence.
Implication and equivalential reducts of basic algebras
A term operation implication is introduced in a given basic algebra and properties of the implication reduct of are treated. We characterize such implication basic algebras and get congruence properties of the variety of these algebras. A term operation equivalence is introduced later and properties of this operation are described. It is shown how this operation is related with the induced partial order of and, if this partial order is linear, the algebra can be reconstructed by means of...
Integral closure in MV-algebras.
We study the consequences of assuming on an MV-algebra A that Σnnx exists for each x belonging to A.
Interior and closure operators on bounded residuated lattices
Bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate multiplicative interior and additive closure operators (mi- and ac-operators) generalizing topological interior and closure operators on such algebras. We describe connections between mi- and ac-operators, and for residuated lattices with Glivenko property we give connections between operators on them and on the residuated...
Interior and closure operators on bounded residuated lattice ordered monoids
-algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior -algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on -monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on -algebras.
Interior and Closure Operators on Commutative Bounded Residuated Lattices
Commutative bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate additive closure and multiplicative interior operators on this class of algebras.
Intersection preserving and global expansions of subalgebras and filters in lattice implication algebras.
Inverse topology in MV-algebras
We introduce the inverse topology on the set of all minimal prime ideals of an MV-algebra and show that the set of all minimal prime ideals of , namely , with the inverse topology is a compact space, Hausdorff, -space and -space. Furthermore, we prove that the spectral topology on is a zero-dimensional Hausdorff topology and show that the spectral topology on is finer than the inverse topology on . Finally, by open sets of the inverse topology, we define and study a congruence relation...
Isometries and direct decompositions of pseudo MV-algebras
Isometries of generalized -algebras
In this paper we investigate the relations between isometries and direct product decompositions of generalized -algebras.
Isometries of -algebras