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Algebra and Discrete Mathematics, 2008, Issue 4, Pages 15–22
(Mi adm175)
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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
On tame semigroups generated by idempotents with partial null multiplication
Vitaliy M. Bondarenkoa, Olena M. Tertychnab a Institute of Mathematics, NAS, Kyiv, Ukraine
b Kyiv National Taras Shevchenko University, Kiev, Ukraine
Abstract:
Let $I$ be a finite set without $0$ and $J$ a subset in $I\times I$ without diagonal elements $(i,i)$. We define $S(I,J)$ to be the semigroup with generators $e_i$, where $i\in I\cup 0$, and the following relations: $e_0=0$; $e_i^2=e_i$ for any $i\in I$; $e_ie_j=0$ for any $(i,j)\in J$. In this paper we study finite-dimensional representations of such semigroups over a field $k$. In particular, we describe all finite semigroups $S(I,J)$ of tame representation type.
Keywords:
semigroup, representation, tame type, the Tits form.
Received: 13.05.2008 Revised: 14.10.2008
Citation:
Vitaliy M. Bondarenko, Olena M. Tertychna, “On tame semigroups generated by idempotents with partial null multiplication”, Algebra Discrete Math., 2008, no. 4, 15–22
Linking options:
https://www.mathnet.ru/eng/adm175 https://www.mathnet.ru/eng/adm/y2008/i4/p15
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Abstract page: | 105 | Full-text PDF : | 59 | First page: | 1 |
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