2023
DOI: 10.1142/s0219498824501342
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On the theory and applications of G-dimension with respect to a semidualizing module

Abstract: We contribute to the theory of G-dimension relative to a semidualizing module [Formula: see text], in connection to the properties of a module being totally [Formula: see text]-reflexive, [Formula: see text]-[Formula: see text]-torsionless, and [Formula: see text]-[Formula: see text]-syzygy, where [Formula: see text] is an integer. We extend several known results, and for an integer [Formula: see text] we introduce the class of [Formula: see text]-[Formula: see text]-Gorenstein rings. We also consider [Formula… Show more

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