A new monoid construction under crossed products

Abstract

In this paper we define a new monoid construction under crossed products for given monoids. We also present a generating set and a relator set for this product. Finally, we give the necessary and sufficient conditions for the regularity of it. MSC: 05C10; 05C12; 05C25; 20E22; 20M05

Semigroup Construction on Polygonal Numbers

“…Corollary 3.1 Let 𝑀𝑀 be the set of sequence of numbers 𝑆𝑆 𝑚𝑚 (𝑛𝑛) and let * a binary operation on 𝑀𝑀(defined in (7)) such that,…”

“…In addition, it will be investigated whether the algebraic structures defined with the general operator specify a semigroup or not. By the way, maybe other algebraic studies, such as the studies in [5][6][7], can be studied by other mathematicians with the binary operation defined on this new algebraic structure.…”

Regularity of n-generalized Schützenberger product of monoids

“…After these works, in [6], the authors determined necessary and sufficient conditions for Schützenberger product of monoids and the new version of the Schützenberger product of monoids to be regular and strongly  -inverse. Furthermore, in [3], the authors studied the regularity of a new monoid construction under crossed and Schützenberger product to any two monoids. In this study, as the main result of this paper, we give an answer by defining necessary and sufficient conditions of the ngeneralized Schützenberger product 12 n A A A    to be regular where all (1 ) i A i n  are any monoids.…”

Crossed product of infinite groups and complete rewriting systems

“…The reader is referred to [7][8][9]11] for recent studies on crossed product of groups and its derivations.…”