ON ALMOST NIL-INJECTIVE RINGS

Abstract

Let R be a ring. The ring R is called right almost nil-injective, if for any a ∈ N(R), there exists a left ideal Xa of R such that lr(a) = Ra ⊕ Xa. In this paper, we give some characterizations and properties of almost nilinjective rings, which is a proper generalization of AP-injective ring and almost mininjective ring. And we study the regularity of right almost nil-injective ring, and in the same time, when every simple singular right R−module is almost nil-injective, we also give some properties of R .