Gröbner–Shirshov bases of some monoids

Abstract

The main goal of this paper is to define Gröbner–Shirshov bases for some monoids.\ud Therefore, after giving some preliminary material, we first give Gröbner–Shirshov bases for\ud graphs and Schützenberger products of monoids in separate sections. In the final section,\ud we further present a Gröbner–Shirshov basis for a Rees matrix semigroup

Gröbner–Shirshov bases and their calculation

“…5 is for -algebras and operads. 7 To conclude this introduction, we give some information about the work of Shirshov; for more on this, see the book [209]. Shirshov (1921Shirshov ( -1981) was a famous Russian mathematician.…”

Gröbner-Shirshov Bases of Some Semigroup Constructions

“…[26] Suppose that semigroups S and T have presentations A |P and B|Q , respectively. Also assume that they are acting on each other as in (1). Then S ⊗ T has a presentation A, B | P, Q, {(ba, b ab a ) : a ∈ A i , b ∈ Bν} such that ν is the normal form function.…”

“…One of these areas is the structure theory of completely (0)-simple semigroups (see, for example, [21]). Actually, the main result of this section will be given as an application of [1,Theorem 12].…”

Базисы Грeбнера - Ширшова для расширенных модулярных групп, расширенных групп Гекке и групп Пикара

“…Читатель может ознакомиться с другими важными результатами о базисах Грёбнера-Ширшова в [6], [9]- [14]. (где -группа диэдра с 2 элементами) и имеет копредставление…”