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independence algebras

Proceedings of the Edinburgh Mathematical Society (1)

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NORMAL SEMIGROUPS OF ENDOMORPHISMS OF PROPER INDEPENDENCE ALGEBRAS ARE IDEMPOTENT GENERATED
João Araújo
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 45 / Issue 1 / February 2002

Published online by Cambridge University Press:

05 February 2002, pp. 205-217
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Let $\mathcal{A}$ be a proper independence algebra of finite rank, let $G$ be the group of automorphisms of $\mathcal{A}$, let $a$ be a singular endomorphism and let $a^G$ be the semigroup generated by all the elements $g^{-1}ag$, where $g\in G$. The aim of this paper is to prove that $a^G$ is a semigroup generated by its own idempotents.
AMS 2000 Mathematics subject classification: Primary 20M20; 20M10; 08A35