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