Generators and relations of Rees matrix semigroups

H Ayik; Nikola Ruskuc

doi:10.1017/S0013091500020472

Generators and relations of Rees matrix semigroups

H Ayik, Nikola Ruskuc

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we consider finite generation and finite presentability of Rees matrix semigroups (with or without zero) over arbitrary semigroups. The main result states that a Rees matrix semigroup M[S; I, J; P] is finitely generated (respectively, finitely presented) if and only if S is finitely generated (respectively, finitely presented), and the sets I, J and S\U are finite, where U is the ideal of S generated by the entries of P.

Original language	English
Pages (from-to)	481-495
Number of pages	15
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	42
Issue number	3
DOIs	https://doi.org/10.1017/S0013091500020472
Publication status	Published - Oct 1999

Keywords

SUBSEMIGROUPS

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10.1017/S0013091500020472

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AB - In this paper we consider finite generation and finite presentability of Rees matrix semigroups (with or without zero) over arbitrary semigroups. The main result states that a Rees matrix semigroup M[S; I, J; P] is finitely generated (respectively, finitely presented) if and only if S is finitely generated (respectively, finitely presented), and the sets I, J and S\U are finite, where U is the ideal of S generated by the entries of P.

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Generators and relations of Rees matrix semigroups

Abstract

Keywords

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