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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2012 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/152236 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862638108026077184 |
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| author | Bondarenko, V. Tertychna, O. |
| author_facet | Bondarenko, V. Tertychna, O. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-11-30T23:11:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152236 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-30T23:11:30Z |
| publishDate | 2012 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Bondarenko, V. Tertychna, O. 2019-06-09T06:05:53Z 2019-06-09T06:05:53Z 2012 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. https://nasplib.isofts.kiev.ua/handle/123456789/152236 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents Article published earlier |
| spellingShingle | On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents Bondarenko, V. Tertychna, O. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152236 |
| work_keys_str_mv | AT bondarenkov on0semisimplicityoflinearhullsofgeneratorsforsemigroupsgeneratedbyidempotents AT tertychnao on0semisimplicityoflinearhullsofgeneratorsforsemigroupsgeneratedbyidempotents |