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Proceedings of the American Mathematical Society

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

 

 

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 $ M$ be a connected regular linear algebraic monoid with zero and group of units $ G$. Suppose $ G$ is nearly simple, i.e. the center of $ G$ is one dimensional and the derived group $ G'$ is a simple algebraic group. Then it is shown that $ S = M\backslash G$ is an idempotent generated semigroup. If $ M$ has a unique nonzero minimal ideal, the converse is also proved. It follows that if $ {G_0}$ is any simple algebraic group defined over an algebraically closed field $ K$ and if $ \Phi :{G_0} \to GL(n,K)$ is any representation of $ {G_0}$, then the nonunits of the monoid $ M(\Phi ) = \overline {K\Phi ({G_0})} $ 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