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\(\mathcal{K}\),...
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| Date: | 2015 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2015
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/97 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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 \(3\). |
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