Geodesic
On finiteness conditions for Rees matrix semigroups
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 455-463
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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.
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.
Classification : 20M05, 20M10
Keywords: Rees matrix semigroup; periodicity; local finiteness; residual finiteness; word problem 
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Ayik, Hayrullah. On finiteness conditions for Rees matrix semigroups. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 455-463. http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a14/

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