ON ALMOST NIL-INJECTIVE RINGS

Year 2011, Volume: 9 Issue: 9, 103 - 113, 01.06.2011

Zhao Yu-e Du Xianneng

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 .

Keywords

almost nil-injective ring, nil-injective ring, n-regular ring, almost mininjective ring

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• School of Mathematics and Computational Science Anhui University Heifei, China e-mail: [e-mail]