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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Збережено в:
Бібліографічні деталі
Дата:2012
Автори: Bondarenko, V., Tertychna, O.
Формат: Стаття
Мова:English
Опубліковано: Інститут прикладної математики і механіки НАН України 2012
Назва видання:Algebra and Discrete Mathematics
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/152236
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Резюме: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.