Regularity of n-generalized Schützenberger product of monoids

Abstract

In this work, regularity of $n$-generalized Schützenberger product of monoids from the point of Group Theory is studied. Here, it is determined necessary and sufficient conditions of the $n$-generalized Schützenberger product $A_{1}\Diamond A_{2}\Diamond \cdots \Diamond A_{n}$ to be regular while all $A_{i}\text{ }\left( 1\leqslant i\leqslant n\right)$ are monoids. Also, by considering all $A_{i}\text{ }\left( 1\leqslant i\leqslant n\right)$ to be groups, it is given another result for the regularity of this product.