Geodesic
On tame semigroups generated by idempotents with partial null multiplication
Algebra and discrete mathematics, no. 4 (2008), pp. 15-22.

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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, the Tits form.
Mots-clés : tame type 
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     author = {Vitaliy M. Bondarenko and Olena M. Tertychna},
     title = {On tame  semigroups generated by idempotents with partial null multiplication},
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     pages = {15--22},
     publisher = {mathdoc},
     number = {4},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2008_4_a2/}
}
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Vitaliy M. Bondarenko; Olena M. Tertychna. On tame  semigroups generated by idempotents with partial null multiplication. Algebra and discrete mathematics, no. 4 (2008), pp. 15-22. http://geodesic.mathdoc.fr/item/ADM_2008_4_a2/