A note on commutative weakly nil clean rings

Abstract

In this paper we discuss some properties of abelian (weakly) nil clean rings. We prove that any subring of an abelian (weakly) nil clean ring is (weakly) nil clean (Theorem 2). We also show that the tensor product of commutative (weakly) nil clean rings is also (weakly) nil clean and give sufficient conditions for the converse to be true (Theorems 3–6).