| 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:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127991 |
| . |
| Reference:
|
[1] H. Ayık and N. Ruškuc: Generators and relations of Rees matrix semigroups.Proc. Edinburgh Math. Soc. 42 (1999), 481–495. MR 1721767 |
| Reference:
|
[2] É. A. Golubov: Finitely separable and finitely approximatable full 0-simple semigroups.Math. Notes 12 (1972), 660–665. 10.1007/BF01093670 |
| Reference:
|
[3] J. M. Howie: Fundamentals of Semigroup Theory.Oxford University Press, Oxford, 1995. Zbl 0835.20077, MR 1455373 |
| Reference:
|
[4] M. V. Lawson: Rees matrix semigroups.Proc. Edinburgh Math. Soc. 33 (1990), 23–37. Zbl 0668.20049, MR 1038762 |
| Reference:
|
[5] J. Meakin: Fundamental regular semigroups and the Rees construction.Quart. J. Math. Oxford 33 (1985), 91–103. Zbl 0604.20060, MR 0780353 |
| Reference:
|
[6] D. Rees: On semi-groups.Proc. Cambridge Philos. Soc. 36 (1940), 387–400. Zbl 0028.00401, MR 0002893 |
| Reference:
|
[7] N. Ruškuc: On large subsemigroups and finiteness conditions of semigroups.Proc. London Math. Soc. 76 (1998), 383–405. MR 1490242 |
| Reference:
|
[8] E. F. Robertson, N. Ruškuc and J. Wiegold: Generators and relations of direct products of semigroups.Trans. Amer. Math. Soc. 350 (1998), 2665–2685. MR 1451614, 10.1090/S0002-9947-98-02074-1 |
| . |
