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Given an independence algebra 4 of infinite rank, we denote the endomorphism monoid and the automorphism group of A by End(A) and Aut(A), respectively. This paper is conceed with finding minimal subsets R of End(A) such that Aut(A) ∪ E(End(A)) ∪ R is a generating set for End(A), where E(End(A))denotes its set of idempotents.