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This paper is concerned with algebras generated by two idempotents P and Q satisfying (PQ)m=(QP)m and (PQ)m-1≠(QP)m-1. The main result is the classification of all these algebras, implying that for each m⩾2 there exist exactly eight nonisomorphic copies. As an application, it is shown that if an element of such an algebra has a nondegenerate leading term, then it is group invertible, and a formula...
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