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
The goal of this paper is to establish a new class of semigroups based on both Rees matrix and completely [Formula: see text]-simple semigroups. We further present some fundamental properties and finiteness conditions for this new semigroup structure.
In this paper, we obtain a complete rewriting system for monoid presentation of Schützenberger product of [Formula: see text] groups, which is firstly defined in [G. M. S. Gomes, H. Sezinando and J. E. Pin, Presentations of the Schützenberger product of [Formula: see text] groups, Comm. Algebra 34(4) (2006) 1213–1235]. It gives an algorithm for getting normal form of elements and hence solving the word problem in this group.
In this paper, we first define a new version of the crossed product of groups under the name of two-sided crossed product. Then we present a generating and relator sets for this new product over cyclic groups. In a separate section, by using the monoid presentation of the two-sided crossed product of cyclic groups, we obtain the complete rewriting system and normal forms of elements of this new group construction.
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