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Vietnam Journal of Mathematics 33:1 (2005) 97-110

New Characterizations and Generalizations

of PP Rings

Lixin Mao, Nanqing Ding, and Wenting Tong

Abstract. This paper consists of two parts. In the first part, it is proven that a ring R is right PP if and only if every right R-module has a monic PI-cover, where PI denotes the class of all P-injective right R-modules. In the second part, for a nonempty subset X of a ring R, we introduce the notion of X-PP rings which unifies PP rings, PS rings and nonsingular rings. Special attention is paid to J-PP rings, where J is the Jacobson radical of R. It is shown that right J-PP rings lie strictly between right PP rings and right PS rings. Some new characterizations of (von Neumann) regular rings and semisimple Artinian rings are also given.

 

 

 

 

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