We first give some useful characterizations of regular semigroups and right weakly regular semigroups by the properties of their bi-ideals, interior ideals, left ideals and right ideals. Based on these characterizations, we also characterize regular semigroups and right weakly regular semigroups by the properties of their (∈,∈ ∨qk)-fuzzy (generalized) bi-ideals, (∈,∈ ∨qk)-fuzzy interior ideals,...

let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

Let A be a finite alphabet and let L ⊂ (A∗)n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an asynchronous n-tape automaton, and it is weakly regular if it is accepted by a non-deterministic asynchronous n-tape automaton. We investigate the closure properties of t...

We apply minimal weakly generating sets to study the existence of Add ( U R ) -covers for a uniserial module . If is right over ring , then S : = End has at most two maximal (right, left, two-sided) ideals: one set I all endomorphisms that are not injective, and other K surjective. prove if either finitely generated, or artinian, ? class covering only it closed under direct limit. Moreover, we ...

Let A be a finite alphabet and let L ⊂ (A∗)n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an asynchronous n-tape automaton, and it is weakly regular if it is accepted by a non-deterministic asynchronous n-tape automaton. We investigate the closure properties of t...

We discuss various properties of a ring over which each simple module is Σ-injective. We shall consider associative rings with identity. Our modules will be unital right modules unless stated otherwise. The class of right V rings was introduced by Villamayor [20]. A ring R is called a right V ring if each simple right Rmodule is injective. It is a well-known unpublished result due to Kaplansky ...

This article extends results on regular implementablity in [3] and [8] to the case when the signal space is not an injective cogenerator, for instance, the space D of compactly supported smooth functions on R. In this case the bijective correspondence between behaviors and modules fails to hold; also projections and sums of behaviors need not in general be behaviors. A more general version of i...

1 We show that, for any regular Poisson manifold, there is an injective natural linear map from the first leafwise cohomology space into the first Poisson cohomology space which maps the Reeb class of the symplectic foliation to the modular class of the Poisson manifold. The Riemannian interpretation of those classes will permit us to show that a regular Poisson manifold whose symplectic foliat...

The purpose of this paper is to study the local structure semi-invariant picture a tame hereditary algebra near null root. Using construction that we call co-amalgamation, show completely described by pictures collection self-injective Nakayama algebras. We then describe cones using cluster-like structures support regular clusters. Finally, (piecewise linearly) invariant under cluster tilting.

The purpose of this paper is to introduce and study the concepts of intuitionistic fuzzy perfectly regular weakly generalized continuous mappings and intuitionistic fuzzy perfectly regular weakly generalized open mappings in intuitionistic fuzzy topological space. Some of their properties are explored.