On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents
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| Creator |
Bondarenko, V.
Tertychna, O. |
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| 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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| Date |
2019-06-09T06:05:53Z
2019-06-09T06:05:53Z 2012 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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