JP Journal of Algebra, Number Theory and Applications
Volume 39, Issue 1, Pages 77 - 86
(February 2017) http://dx.doi.org/10.17654/NT039010077 |
|
SEMIGROUPS WITH MAXIMUM COMMUTING REGULARITY DEGREE
A. Firuzkuhy and H. Doostie
|
Abstract: The commuting regularity degree, of a non-group semigroup S is defined and studied recently by Firuzkuhy and Doostie in [7], where is the probability that a pair of the elements of S is a commuting regular pair (the pair is called a commuting regular pair if for some element This definition is an identifier in characterization of the commuting regular semigroups specially when they are non-group. When then S is called a commuting regular semigroup. Among all of the recent studies on non-group non-commutative semigroups, is less than or equal A natural question is finding finite non-group non-commutative semigroups for which dcr achieves the maximum value. In this paper, we prove that for a non-group regular quasi-commutative semigroup S, Moreover, the converse does not hold. Indeed, by considering the infinite class of finitely presented semigroups
of order we show that for every however, is non-regular and non quasi-commutative, where a semigroup S is said to be quasi-commutative if for all there exists a positive integer r such that Our final results concerning are about the direct and semidirect products of finite semigroups. |
Keywords and phrases: monogenic semigroups, direct product, commuting regularity degree. |
|
Number of Downloads: 487 | Number of Views: 1667 |
|