PSEUDO QP-INJECTIVE MODULES AND GENERALIZED PSEUDO QP-INJECTIVE MODULES
Let M be a right R-module with S = End(MR). Then MR is called pseudo QP-injective (or P QP-injective for short) if every monomorphism from an M-cyclic submodule of M to M extends to an endomorphism of M . MR is called generalized pseudo QP-injective (or GP QP-injective for short) if, for any 0 6= s ∈ S, there exists a positive integer n such that s n 6= 0 and every monomorphism from snM to M extends to an endomorphism of M. Characterizations and properties of the two classes of modules are studied. The two classes of modules with some additional conditions are studied, semisimple artinian rings are characterized by P QP-injective modules.
Keywords:
P QP-injective modules, GP QP-injective modules, endomorphism rings, semisimple artinian rings perfect rings,
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- Department of Mathematics Jiaxing University Jiaxing, Zhejiang Province, P.R.China e-mail: zhanmin zhu@hotmail.com
- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI
Sayıdaki Diğer Makaleler
Guo ZHONG, Liying YANG, Xuanlong MA, Shixun LİN