ON ALMOST NIL-INJECTIVE RINGS

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International Electronic Journal of Algebra
Volume:9 Issue:9
ON ALMOST NIL-INJECTIVE RINGS

ON ALMOST NIL-INJECTIVE RINGS

Authors : Zhao Yue, Du Xianneng

Pages : 103-113

View : 21 | Download : 9

Publication Date : 2011-06-01

Article Type : Research Paper

Abstract :Let R be a ring. The ring R is called right almost nil-injective, if for any a ∈ Ninsert ignore into journalissuearticles values(R);, there exists a left ideal Xa of R such that lrinsert ignore into journalissuearticles values(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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