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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| Дата: | 2015 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2015
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/97 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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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