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 × I without diagonal elements. Let S(I, J) denotes the semigroup generated by e₀ = 0 and ei, i ∈ I, with the following relations: e²i = ei for any i ∈ I, eiej = 0 for any (i, j) ∈ J. In this paper we prove that, for any finite semigroup S = S(I...
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| Видавець: | Інститут прикладної математики і механіки НАН України |
|---|---|
| Дата: | 2012 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2012
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152236 |
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| Цитувати: | On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents / V. Bondarenko, O. Tertychna // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 168–173. — Бібліогр.: 3 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-152236 |
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dspace |
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irk-123456789-1522362019-06-10T01:26:16Z On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents Bondarenko, V. Tertychna, O. Let I be a finite set (without 0) and J a subset of I × I without diagonal elements. Let S(I, J) denotes the semigroup generated by e₀ = 0 and ei, i ∈ I, with the following relations: e²i = ei for any i ∈ I, eiej = 0 for any (i, j) ∈ 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 ∑i∈IαiM(ei) with αi ∈ 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. 2012 Article On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents / V. Bondarenko, O. Tertychna // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 168–173. — Бібліогр.: 3 назв. — англ. 1726-3255 2010 MSC:16G, 20M30. http://dspace.nbuv.gov.ua/handle/123456789/152236 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Let I be a finite set (without 0) and J a subset of I × I without diagonal elements. Let S(I, J) denotes the semigroup generated by e₀ = 0 and ei, i ∈ I, with the following relations: e²i = ei for any i ∈ I, eiej = 0 for any (i, j) ∈ 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 ∑i∈IαiM(ei) with αi ∈ 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. |
| format |
Article |
| author |
Bondarenko, V. Tertychna, O. |
| spellingShingle |
Bondarenko, V. Tertychna, O. On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents Algebra and Discrete Mathematics |
| author_facet |
Bondarenko, V. Tertychna, O. |
| author_sort |
Bondarenko, V. |
| title |
On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents |
| title_short |
On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents |
| title_full |
On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents |
| title_fullStr |
On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents |
| title_full_unstemmed |
On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents |
| title_sort |
on 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152236 |
| citation_txt |
On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents / V. Bondarenko, O. Tertychna // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 2. — С. 168–173. — Бібліогр.: 3 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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AT bondarenkov on0semisimplicityoflinearhullsofgeneratorsforsemigroupsgeneratedbyidempotents AT tertychnao on0semisimplicityoflinearhullsofgeneratorsforsemigroupsgeneratedbyidempotents |
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2023-05-20T17:37:49Z |
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