Matrix semigroups

Author:
Mohan S. Putcha

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

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Abstract: Let 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 of such that , is completely simple, and each Rees factor semigroup , , is either completely 0-simple or else a nilpotent semigroup. The basic technique is to study the Zariski closure of , which is a linear algebraic semigroup.

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Additional Information

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