| Title:
|
Properties of the subsemigroups of the bicyclic monoid (English) |
| Author:
|
Descalço, L. |
| Author:
|
Ruškuc, N. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
311-330 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study some properties of the subsemigroups of the bicyclic monoid B, by using a recent description of its subsemigroups. We start by giving necessary and sufficient conditions for a subsemigroup to be finitely generated. Then we show that all finitely generated subsemigroups are automatic and finitely presented. Finally we prove that a subsemigroup of B is residually finite if and only if it does not contain a copy of B. (English) |
| Keyword:
|
bicyclic monoid |
| Keyword:
|
subsemigroup |
| Keyword:
|
generators |
| Keyword:
|
defining relations |
| Keyword:
|
automatic structures |
| MSC:
|
20M05 |
| MSC:
|
20M10 |
| idZBL:
|
Zbl 1166.20052 |
| idMR:
|
MR2411092 |
| . |
| Date available:
|
2009-09-24T11:55:01Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128260 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| . |
