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Right orthogonal class of pure projectiv...
Arunachalam, Umamahe...

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Right orthogonal class of pure projective modules over pure hereditary rings by Arunachalam, Umamaheswaran ( Author )
Lemonjar Open Access
N.A
12-05-2016
We denote by W the class of all pure projective modules. Present article we investigate W-injective modules and these modules are defined via the vanishing of cohomology of pure projective modules. First we prove that every module has a W-injective preenvelope and then every module has a W-injective coresolution over an arbitrary ring. Further, we show that the class of all W-injective modules is coresolving (injectively resolving) over a pure-hereditary ring. Moreover, we analyze the dimension of W-injective coresolution over a pure-hereditary ring. It is shown that $\sup\{ \cores_{\mathcal{W}^{\bot}}(M) \colon M \mbox{is an }R\mbox{-module }\} = \Fcor_{\mathcal{W}^{\bot}}(R) = \sup\{\pd(G) \colon G \mbox{ is a pure projective } R\mbox{-module}\}$ and we give some equivalent conditions of W-injective envelope with the unique mapping property. In the last section, we proved the desirable properties of the dimension when the ring is semisimple artinian.
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Article
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36.88 KB
English
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MYR 0.01
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http://arxiv.org/abs/1605.03704
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