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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Matrix semigroups


Author: Mohan S. Putcha
Journal: Proc. Amer. Math. Soc. 88 (1983), 386-390
MSC: Primary 20M10
MathSciNet review: 699399
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0699399-0
Keywords: Matrix semigroup, algebraic semigroup, nil, nilpotent, chain conditions
Article copyright: © Copyright 1983 American Mathematical Society