In this paper we will investigate commutative Bezout domains whose finite homomorphic images are semipotent rings. Among such commutative Bezout rings we consider a new class of rings and call them an effective rings. ...

The (proper) power graph of a group is a graph whose vertex set is the set of all (nontrivial) elements of the group and two distinct vertices are adjacent if one is a power of the other. Various kinds of planarity of ...

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 endomorphism of Cay(S,A) if for each (x, y) ∈ E(Cay(S,A)) ...

In this manuscript, we have evaluated the energies of Smith graphs. In the course of the investigation, we found that only one Smith graph is hypo-energetic. Moreover, we have also established the energy bounds for Smith graphs.

We introduce the equivalence relation ρ on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing l-cycles with l>4 to an equivalent Carter diagram containing only 4-cycles. ...

Let q be a prime power and k∈{5,7,9,11}. In this paper it is shown that the girth of a graph D(k,q) is equal to k+5. As a consequence, explicit examples of graphs which provide the best known upper bounds of the order of ...

We give a survey of results connecting the exponent matrices with Frobenius rings. In particular, we prove that for any parmutation σ ∈ Sn there exists a countable set of indecomposable Frobenius semidistributive rings Am ...

The Partition algebras Pk(x) have been defined in [M1] and [Jo]. We introduce a new class of algebras for every group G called “Extended G-Vertex Colored Partition Algebras," denoted by Pbk(x,G), which contain partition ...

We extend the classical theory of factorization in noncommutative integral domains to the more general classes of right saturated rings and right cyclically complete rings. Our attention is focused, in particular, on the ...

The famous Ukrainian mathematician and educator, Doctor of Physical and Mathematical Sciences, Professor Fedir Mykolayovych Lyman passed away on June 13, 2020 after a long illness.