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Idempotent generated endomorphisms of an independence Algebra

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The aim of this note is to give a direct proof for the following result proved by Fountain and Lewin: Let A be an independence algebra of finite rank and let a be a singular endomorphism of A. Then a = e1 . . . en where e2i = ei and rank(a) = rank(ei).

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Araújo, João - Idempotent generated endomorphisms of an independence Algebra. "Semigroup Forum" [Em linha]. ISSN 0037-1912 (Print) 1432-2137 (Online). Vol. 67 (2003), p. 1-4

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