Communications of the
Korean Mathematical Society CKMS

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.

Keywords: idempotent, nilpotent, involution, nil-clean ring of nilpotency index at most $2$, involution-clean ring

MSC numbers: Primary 16U60