Algebraic monoids whose nonunits are products of idempotents

Author:
Mohan S. Putcha

Journal:
Proc. Amer. Math. Soc. **103** (1988), 38-40

MSC:
Primary 20M10

DOI:
https://doi.org/10.1090/S0002-9939-1988-0938640-8

MathSciNet review:
938640

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Abstract: Let be a connected regular linear algebraic monoid with zero and group of units . Suppose is nearly simple, i.e. the center of is one dimensional and the derived group is a simple algebraic group. Then it is shown that is an idempotent generated semigroup. If has a unique nonzero minimal ideal, the converse is also proved. It follows that if is any simple algebraic group defined over an algebraically closed field and if is any representation of , then the nonunits of the monoid form an idempotent generated semigroup.

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0938640-8

Article copyright:
© Copyright 1988
American Mathematical Society