On n-f-Semiclean Rings

Abstract

The class of n-f-semiclean rings lies between the classes of n-f-clean rings and \((n+1)\)-f-clean rings. We give a characterization of n-f-semiclean rings in terms of its Pierce stalks. We prove that if e is an idempotent such that eRe and \((1-e)R(1-e)\) are n-f-semiclean, then R is n-f-semiclean. Further, we find that matrix rings of an n-f-semiclean ring are n-f-semiclean. We give some characterizations of n-f-semiclean rings in terms of their extension rings.