On \(0\)-semisimplicity of linear hulls of generators for semigroups generated by idempotents
Let \(I\) be a finite set (without \(0\)) and \(J\) a subset of \(I\times I\) without diagonal elements. Let \(S(I,J)\) denotes the semigroup generated by \(e_0=0\) and \(e_i\), \(i\in I\), with the following relations: \(e_i^2=e_i\) for any \(i\in I\), \(e_ie_j=0\) for any \((i,j)\in J\). In thi...
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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/718 |
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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 of \(I\times I\) without diagonal elements. Let \(S(I,J)\) denotes the semigroup generated by \(e_0=0\) and \(e_i\), \(i\in I\), with the following relations: \(e_i^2=e_i\) for any \(i\in I\), \(e_ie_j=0\) for any \((i,j)\in J\). In this paper we prove that, for any finite semigroup \(S=S(I,J)\) and any its matrix representation \(M\) over a field \(k\), each matrix of the form \(\sum_{i \in I}\alpha_i M(e_i)\) with \(\alpha_i\in k\) is similar to the direct sum of some invertible and zero matrices. We also formulate this fact in terms of elements of the semigroup algebra. |
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