On characteristic properties of semigroups
Let \(\mathcal{K}\) be a class of semigroups and \(\mathcal{P}\) be a set of general properties of semigroups. We call a subset \(Q\) of \(\mathcal{P}\) cha\-racteristic for a semigroup\(S\in\mathcal{K}\) if, up to isomorphism and anti-isomorphism, \(S\) is the only semigroup in\(\mathcal{K}\),...
Gespeichert in:
| Datum: | 2015 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2015
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/97 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| id |
oai:ojs.admjournal.luguniv.edu.ua:article-97 |
|---|---|
| record_format |
ojs |
| spelling |
oai:ojs.admjournal.luguniv.edu.ua:article-972015-11-10T19:25:54Z On characteristic properties of semigroups Bondarenko, Vitaliy M. Zaciha, Yaroslav V. semigroup, anti-isomorphism, idempotent, Cayley table, characteristic property, char-complete set 20M Let \(\mathcal{K}\) be a class of semigroups and \(\mathcal{P}\) be a set of general properties of semigroups. We call a subset \(Q\) of \(\mathcal{P}\) cha\-racteristic for a semigroup\(S\in\mathcal{K}\) if, up to isomorphism and anti-isomorphism, \(S\) is the only semigroup in\(\mathcal{K}\), which satisfies all the properties from \(Q\). The set of properties \(\mathcal{P}\) is called char-complete for \(\mathcal{K}\) if for any \(S\in \mathcal{K}\)the set of all properties\(P\in\mathcal{P}\), which hold for the semigroup \(S\), is characteristic for \(S\).We indicate a 7-element set of properties of semigroups which is a minimal char-complete setfor the class of semigroups of order \(3\). Lugansk National Taras Shevchenko University 2015-11-09 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/97 Algebra and Discrete Mathematics; Vol 20, No 1 (2015): A special issue 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/97/27 Copyright (c) 2015 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2015-11-10T19:25:54Z |
| collection |
OJS |
| language |
English |
| topic |
semigroup anti-isomorphism idempotent Cayley table characteristic property char-complete set 20M |
| spellingShingle |
semigroup anti-isomorphism idempotent Cayley table characteristic property char-complete set 20M Bondarenko, Vitaliy M. Zaciha, Yaroslav V. On characteristic properties of semigroups |
| topic_facet |
semigroup anti-isomorphism idempotent Cayley table characteristic property char-complete set 20M |
| format |
Article |
| author |
Bondarenko, Vitaliy M. Zaciha, Yaroslav V. |
| author_facet |
Bondarenko, Vitaliy M. Zaciha, Yaroslav V. |
| author_sort |
Bondarenko, Vitaliy M. |
| title |
On characteristic properties of semigroups |
| title_short |
On characteristic properties of semigroups |
| title_full |
On characteristic properties of semigroups |
| title_fullStr |
On characteristic properties of semigroups |
| title_full_unstemmed |
On characteristic properties of semigroups |
| title_sort |
on characteristic properties of semigroups |
| description |
Let \(\mathcal{K}\) be a class of semigroups and \(\mathcal{P}\) be a set of general properties of semigroups. We call a subset \(Q\) of \(\mathcal{P}\) cha\-racteristic for a semigroup\(S\in\mathcal{K}\) if, up to isomorphism and anti-isomorphism, \(S\) is the only semigroup in\(\mathcal{K}\), which satisfies all the properties from \(Q\). The set of properties \(\mathcal{P}\) is called char-complete for \(\mathcal{K}\) if for any \(S\in \mathcal{K}\)the set of all properties\(P\in\mathcal{P}\), which hold for the semigroup \(S\), is characteristic for \(S\).We indicate a 7-element set of properties of semigroups which is a minimal char-complete setfor the class of semigroups of order \(3\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2015 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/97 |
| work_keys_str_mv |
AT bondarenkovitaliym oncharacteristicpropertiesofsemigroups AT zacihayaroslavv oncharacteristicpropertiesofsemigroups |
| first_indexed |
2025-07-17T10:34:05Z |
| last_indexed |
2025-07-17T10:34:05Z |
| _version_ |
1837889953965539328 |