DP-PROJECTIVE MODULES AND DIMENSIONS

Abstract

In this paper, we introduce the notion of DP-projective modules. It is shown that a left R-module M over a ring R is DP-projective if and only if it is a cokernel of a Ding projective preenvelope f : A → B with B projective. It is also shown that a ring R is semisimple if and only if every module is DP-projective. Moreover, we investigate (global) DP-projective dimensions of modules and rings. It is shown that l.DP-dim(R) = l.DP-ID(R). In addition, other applications of those dimensions defined in this way are presented.

Keywords

• DP-projective module, semisimple ring, DP-projective dimension

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18. School of Mathematics and Computer Science Hubei University Wuhan, Hubei, People’s Republic of China e-mail: [e-mail]