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NORMAL SEMIGROUPS OF ENDOMORPHISMS OF PROPER INDEPENDENCE ALGEBRAS ARE IDEMPOTENT GENERATED

Published online by Cambridge University Press:  05 February 2002

João Araújo
João Araújo
Affiliation:
Universidade Aberta, R. da Escola Politécnica, 147, 1269–001 Lisboa, Portugal Centro de Álgebra, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1699 Lisboa Codex, Portugal ([email protected])
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Abstract

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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

Keywords

independence algebrasnormal semigroupsendomorphisms
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 1 , February 2002 , pp. 205 - 217
Copyright
Copyright © Edinburgh Mathematical Society 2002