NORMAL SEMIGROUPS OF ENDOMORPHISMS OF PROPER INDEPENDENCE ALGEBRAS ARE IDEMPOTENT GENERATED

Abstract

Abstract 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