The balance of relative Ext groups defined by semi dualizing modules

2022/06/18 by Beigi, Kosar Abolfath, Divaani-Aazar, Kamran, Tousi, Massoud
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.09201

Abstract

Let R be a commutative Noetherian ring with identity and C a semidualizing module for R. Let \mathscrP_C(R) and \mathscrI_C (R) denote, respectively, the classes of C-projective and C-injective R-modules. We show that their induced Ext bifunctors Extⁱ_\mathscrP_C(-,∼) and Extⁱ_\mathscrI_C(-,∼) coincide for all i≥ 0 if and only if C is projective. Also, we provide some other criteria for C to be projective by using some special cotorsion theories.

Related

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• Relative Tor functors with respect to a semidualizing module
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• Comparison of relative cohomology theories with respect to semidualizing modules