• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.29-40
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• 2024

Let S and R be rings and _SC_R a semidualizing bimodule. We introduce the notion of G_C-FP_n-injective modules, which generalizes G_C-FP-injective modules and G_C-weak injective modules. The homological properties and the stability of G_C-FP_n-injective modules are investigated. When S is a left n-coherent ring, several nice properties and new Foxby equivalences relative to G_C-FP_n-injective modules are given.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.821-838
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• 2015

We investigate the relative and Tate cohomology theories with respect to Ding modules and complexes, consider their relations with classical and Gorenstein cohomology theories. As an application, the Avramov-Martsinkovsky type exact sequence of Ding modules is obtained.

• Journal of Integrative Natural Science
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• v.4 no.4
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• pp.278-281
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• 2011

We discuss an application of 'restrictions on the entries of the maps in the minimal free resolution' and '$SC_r$-condition of modules', and give an alternative proof of the following result of Foxby: Let M be a finitely generated module of dimension over a Noetherian local ring (A,m). Suppose that $\hat{A}$ has no embedded primes. If A is not Gorenstein, then ${\mu}_i(m,A){\geq}2$ for all i ${\geq}$ dimA.