On tame semigroups generated by idempotents with partial null multiplication
Let \(I\) be a finite set without \(0\) and \(J\) a subset in \(I\times I\) without diagonal elements \((i,i)\). We define \(S(I,J)\) to be the semigroup with generators \(e_i\), where \(i\in I\cup 0\), and the following relations: \(e_0=0\); \(e_i^2=e_i\) for any \(i\in I\); \(e_ie_j=0\) for an...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/824 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | Let \(I\) be a finite set without \(0\) and \(J\) a subset in \(I\times I\) without diagonal elements \((i,i)\). We define \(S(I,J)\) to be the semigroup with generators \(e_i\), where \(i\in I\cup 0\), and the following relations: \(e_0=0\); \(e_i^2=e_i\) for any \(i\in I\); \(e_ie_j=0\) for any \((i,j)\in J\). In this paper we study finite-dimensional representations of such semigroups over a field \(k\). In particular, we describe all finite semigroups \(S(I,J)\) of tame representation type. |
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