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- W3044615206 abstract "Let $mathcal{W}$ be the class of all pure projective modules. In this article, $mathcal{W}$-injective modules is defined via the vanishing of cohomology of pure projective modules. First we show that every module has a $mathcal{W}$-injective coresolution over an arbitrary ring and the class of all $mathcal{W}$-injective modules is coresolving over a pure-hereditary ring. Further, we analyze the dimension of $mathcal{W}$-injective coresolution over a pure-hereditary ring. It is shown that $Fcor_{mathcal{W}^{bot}}(R) = sup{pd(G) colon G$ is a pure projective $R$-module$} = sup{cores_{mathcal{W}^{bot}}(M) colon M $ is an $R$-module$}.$ Finally, we give some equivalent conditions of $mathcal{W}$-injective envelope with the unique mapping property. The dimension has desirable properties when the ring is semisimple artinian." @default.
- W3044615206 created "2020-07-29" @default.
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- W3044615206 date "2016-05-12" @default.
- W3044615206 modified "2023-09-27" @default.
- W3044615206 title "Right orthogonal class of pure projective modules over pure hereditary rings" @default.
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