NIL-CLEAN RINGS OF NILPOTENCY INDEX AT MOST TWO WITH APPLICATION TO INVOLUTION-CLEAN RINGS

摘要

A ring is nil-clean if every element is a sum of a nilpotent and an idempotent, and a ring is involution-clean if every element is a sum of an involution and an idempotent. In this paper, a description of nil-clean rings of nilpotency index at most 2 is obtained, and is applied to improve a known result on involution-clean rings.