ON ALMOST NIL-INJECTIVE RINGS

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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College of Mathematics Qingdao University Qingdao, China e-mail: blueskyyu2004@yahoo.com.cn Du Xianneng
School of Mathematics and Computational Science Anhui University Heifei, China e-mail: xndu@ahu.edu.cn

International Electronic Journal of Algebra-Cover

ISSN: 1306-6048
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2007
Yayıncı: Abdullah HARMANCI

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