Bondarenko, Vitaliy M.Tertychna, Olena M.Тертична, Олена МиколаївнаТертичная, Елена Николаевна2020-08-282020-08-282012Bondarenko V. M. On 0-semisimplicity of linear hulls of generators for semigroups generated by idempotents / Vitaliy M. Bondarenko, Olena M. Tertychna // Algebra and Discrete Mathematics. – 2012. – Vol. 14, № 2. – P. 168–173.1726-3255https://ir.kneu.edu.ua:443/handle/2010/33771Let 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: e2 i = 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 Pmatrix representation M over a field k, each matrix of the form i2I αiM(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.enArticle