Right orthogonal class of pure projective modules over pure hereditary rings

2016/05/12 by Umamaheswaran Arunachalam, Udhayakumar Ramalingam, Arunachalam, Umamaheswaran +5
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1605.03704

Abstract

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_W^\bot(M) \colon M is an R-module \ = \Fcor_W^\bot(R) = sup\\pd(G) \colon G is a pure projective R-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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