On finiteness conditions for Rees matrix semigroups
Czechoslovak Mathematical Journal (2005)
- Volume: 55, Issue: 2, page 455-463
- ISSN: 0011-4642
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topAyik, Hayrullah. "On finiteness conditions for Rees matrix semigroups." Czechoslovak Mathematical Journal 55.2 (2005): 455-463. <http://eudml.org/doc/30958>.
@article{Ayik2005,
abstract = {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.},
author = {Ayik, Hayrullah},
journal = {Czechoslovak Mathematical Journal},
keywords = {Rees matrix semigroup; periodicity; local finiteness; residual finiteness; word problem; Rees matrix semigroups; periodic semigroups; locally finite semigroups; residually finite semigroups; word problem},
language = {eng},
number = {2},
pages = {455-463},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On finiteness conditions for Rees matrix semigroups},
url = {http://eudml.org/doc/30958},
volume = {55},
year = {2005},
}
TY - JOUR
AU - Ayik, Hayrullah
TI - On finiteness conditions for Rees matrix semigroups
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 2
SP - 455
EP - 463
AB - 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.
LA - eng
KW - Rees matrix semigroup; periodicity; local finiteness; residual finiteness; word problem; Rees matrix semigroups; periodic semigroups; locally finite semigroups; residually finite semigroups; word problem
UR - http://eudml.org/doc/30958
ER -
References
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