INSERTION-OF-FACTORS-PROPERTY ON NILPOTENT ELEMENTS

Abstract

We generalize the insertion-of-factors-property by setting nil-potent products of elements. In the process we introduce the concept of a nil-IFP ring that is also a generalization of an NI ring. It is shown that if Kothe's conjecture holds, then every nil-IFP ring is NI. The class of minimal noncommutative nil-IFP rings is completely determined, up to isomorphism, where the minimal means having smallest cardinality.