Matrix semigroups
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- by Mohan S. Putcha PDF
- Proc. Amer. Math. Soc. 88 (1983), 386-390 Request permission
Abstract:
Let $S$ be a semigroup of matrices over a field such that a power of each element lies in a subgroup (i.e., each element has a Drazin inverse within the semigroup). The main theorem of this paper is that there exist ideals ${I_0}, \ldots ,{I_t}$ of $S$ such that ${I_0} \subseteq \cdots \subseteq {I_t} = S$, ${I_0}$ is completely simple, and each Rees factor semigroup ${I_k}/{I_{k - 1}}$, $k = 1, \ldots ,t$, is either completely $0$-simple or else a nilpotent semigroup. The basic technique is to study the Zariski closure of $S$, which is a linear algebraic semigroup.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 386-390
- MSC: Primary 20M10
- DOI: https://doi.org/10.1090/S0002-9939-1983-0699399-0
- MathSciNet review: 699399