Gröbner-Shirshov Bases of the Generalized Bruck-Reilly ∗-Extension

Abstract

In this paper we first define a presentation for the generalized Bruck-Reilly ∗-extension of a monoid and then we work on its Gröbner-Shirshov bases.

Automatic structure for generalized Bruck-Reilly ∗-extension of a monoid

“…In [14], the authors have obtained the following results. [(0; 0; 1 T ; 0; 1)g is a generating set for the monoid GBR (T ; ; ; u).…”

Gröbner-Shirshov basis for the singular part of the Brauer semigroup

“…Furthermore, in [16] and [17], Gröbner-Shirshov bases for Schreier extensions of groups and for the Chinese monoid were defined separately. The reader is referred to [1,5,6,8,19,21,22] for some other recent papers about Gröbner-Shirshov bases.…”

A note on the Gröbner-Shirshov bases over ad-hoc extensions of groups

“…There are some important studies on this subject related to the groups (see, for instance, [8,14]). We may finally refer the papers [4,9,10,18,19] for some other recent studies over Gröbner- Shirshov bases. Algorithmic problems such as the word, conjugacy and isomorphism problems have played an important role in group theory since the work of M. Dehn in early 1900's. These problems are called decision problems which ask for a yes or no answer to a specific question.…”