A weak endomorphisms of a graph is a mapping on the vertex set of the graph which preserves or contracts edges. In this paper we provide a formula to determine the cardinalities of weak endomorphism monoids of finite ...

Let S = K[x1, x2, . . . , xn] be a standard graded K-algebra for any field K. Without using any heavy tools of com- mutative algebra we compute the Hilbert series of graded S-module S/I, where I is a monomial ideal.

We show that the main result of algebraic Morse theory can be obtained as a consequence of the perturbation lemma of Brown and Gugenheim.

We completely determine all commutative semigroup varieties that are cancellable elements of the lattice SEM of all semigroup varieties. In particular, we verify that a commutative semigroup variety is a cancellable element ...

In the present work the relations between the closure operators of two module categories are investigated in the case when the given categories are connected by two covariant adjoint functors H : R-Mod −→ S-Mod and T : ...

For a monounary algebra A = (A, f) we study the lattice Quord A of all quasiorders of A, i.e., of all reflexive and transitive relations compatible with f. Monounary algebras (A, f) whose lattices of quasiorders are ...

Let Cay(S, A) denote the Cayley digraph of the semigroup S with respect to the set A, where A is any subset of S. The function f : Cay(S, A) → Cay(S, A) is called an endo-morphism of Cay(S, A) if for each (x, y) ∈ E(Cay(S, ...

For a given graph G = (V, E), a dominating set D ⊆ V (G) is said to be an outer connected dominating set if D = V (G) or G − D is connected. The outer connected domination number of a graph G, denoted by γec(G), is the ...

This work is devoted to the investigation of module decompositions which arise from Rickart modules, socle and radical of modules. In this regard, the structure and several illustrative examples of inverse split modules ...

In this paper, we introduce the concept of mod- ules with the properties (RE) and (SRE), and we provide various properties of these modules. In particular, we prove that a semisimple module M is Rad-supplementing if ...