RINGS OF COPURE PROJECTIVE DIMENSION ONE

Tao Xiong
2017 Journal of the Korean Mathematical Society  
In this paper, in terms of the notions of strongly copure projective modules and the copure projective dimension cpD(R) of a ring R were defined in [12] , we show that a domain R has cpD(R) ≤ 1 if and only if R is a Gorenstein Dedekind domain. 427 428 T. XIONG where each P i is strongly copure projective. The copure projective dimension of a ring R is defined as In this paper, we characterize some classes of rings in terms of copure projective modules. QF rings, IF rings and semihereditary
more » ... semihereditary rings It was shown in [12, Remark 4.2 & Proposition 3.12] that a ring R is a QF ring if and only if cpD(R) = 0, and if and only if every right R-module is copure projective. Recall that an R-module D is h-divisible if it is an epic image of an injective R-module. As in [4], we call a ring R a right IF ring if every injective right R-module is flat. Now, we characterize QF rings and IF rings in terms of h-divisible modules and copure projective modules.
doi:10.4134/jkms.j160014 fatcat:rqqvhfwnrbdyljl7fh4awdwj2q