On automatic Rees matrix semigroups

L Descalco; Nikola Ruskuc

doi:10.1080/00927870209342378

On automatic Rees matrix semigroups

L Descalco
, Nikola Ruskuc

Research output: Other contribution

Abstract

We consider a Rees matrix semigroup S = M [ U; I, J; P] over a semigroup U, with I and J finite index sets, and relate the automaticity of S with the automaticity of U. We prove that if U is an automatic semigroup and S is finitely generated then S is an automatic semigroup. If S is an automatic semigroup and there is an entry p in the matrix P such that p U-1 = U then U is automatic. We also prove that if S is a prefix-automatic semigroup, then U is a prefix-automatic semigroup.

Original language	English
Volume	30
DOIs	https://doi.org/10.1080/00927870209342378
Publication status	Published - 2002

Keywords

GENERATORS
MONOIDS

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title = "On automatic Rees matrix semigroups",

abstract = "We consider a Rees matrix semigroup S = M [ U; I, J; P] over a semigroup U, with I and J finite index sets, and relate the automaticity of S with the automaticity of U. We prove that if U is an automatic semigroup and S is finitely generated then S is an automatic semigroup. If S is an automatic semigroup and there is an entry p in the matrix P such that p U-1 = U then U is automatic. We also prove that if S is a prefix-automatic semigroup, then U is a prefix-automatic semigroup.",

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T1 - On automatic Rees matrix semigroups

AU - Descalco, L

AU - Ruskuc, Nikola

N1 - Comm Algebra

PY - 2002

Y1 - 2002

N2 - We consider a Rees matrix semigroup S = M [ U; I, J; P] over a semigroup U, with I and J finite index sets, and relate the automaticity of S with the automaticity of U. We prove that if U is an automatic semigroup and S is finitely generated then S is an automatic semigroup. If S is an automatic semigroup and there is an entry p in the matrix P such that p U-1 = U then U is automatic. We also prove that if S is a prefix-automatic semigroup, then U is a prefix-automatic semigroup.

AB - We consider a Rees matrix semigroup S = M [ U; I, J; P] over a semigroup U, with I and J finite index sets, and relate the automaticity of S with the automaticity of U. We prove that if U is an automatic semigroup and S is finitely generated then S is an automatic semigroup. If S is an automatic semigroup and there is an entry p in the matrix P such that p U-1 = U then U is automatic. We also prove that if S is a prefix-automatic semigroup, then U is a prefix-automatic semigroup.

KW - GENERATORS

KW - MONOIDS

UR - https://www.scopus.com/pages/publications/0036013558

U2 - 10.1080/00927870209342378

DO - 10.1080/00927870209342378

M3 - Other contribution

VL - 30

ER -

On automatic Rees matrix semigroups

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Keywords

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