Coreflexive modules and semidualizing modules with finite projective dimension. (English) Zbl 1401.18037

Let \(R\) and \(S\) be two rings, and let \(_R\omega_S\) be a semidualizing bimodule. For a subclass \(\mathcal{T}\) of the class of \(\omega\)-coreflexive modules, the authors introduce and study some objects called modules of \(\omega-\mathcal{T}\)- class \(n\), where \(n\) is a positive integer. These are used to provide information about the projective dimension of \(\omega\) as an \(R\)-module and as an \(S\)-module.


18G25 Relative homological algebra, projective classes (category-theoretic aspects)
16E10 Homological dimension in associative algebras
16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras
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