DP-PROJECTIVE MODULES AND DIMENSIONS

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International Electronic Journal of Algebra
Volume:15 Issue:15
DP-PROJECTIVE MODULES AND DIMENSIONS

DP-PROJECTIVE MODULES AND DIMENSIONS

Pages : 101-116

View : 10 | Download : 12

Publication Date : 2014-06-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(global); DP-projective dimensions of modules and rings. It is shown that l.DP-diminsert ignore into journalissuearticles values(R); = l.DP-IDinsert ignore into journalissuearticles values(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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