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Title: On finiteness conditions for Rees matrix semigroups (English)
Author: Ayik, Hayrullah
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 55
Issue: 2
Year: 2005
Pages: 455-463
Summary lang: English
Category: math
Summary: Let $T=\mathcal {M}[S;I,J;P]$ be a Rees matrix semigroup where $S$ is a semigroup, $I$ and $J$ are index sets, and $P$ is a $J\times I$ matrix with entries from $S$, and let $U$ be the ideal generated by all the entries of $P$. If $U$ has finite index in $S$, then we prove that $T$ is periodic (locally finite) if and only if $S$ is periodic (locally finite). Moreover, residual finiteness and having solvable word problem are investigated. (English)
Keyword: Rees matrix semigroup
Keyword: periodicity
Keyword: local finiteness
Keyword: residual finiteness
Keyword: word problem
MSC: 20M05
MSC: 20M10
idZBL: Zbl 1081.20065
idMR: MR2137151
Date available: 2009-09-24T11:24:24Z
Last updated: 2016-04-07
Stable URL:
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