zbMATH — the first resource for mathematics

Foxby equivalence and cotorsion theories relative to semi-dualizing modules. (English) Zbl 1077.13004
Given a semi-dualizing module the relative Foxby classes can be defined and there is still an associated Foxby duality; the authors consider these classes and two naturally defined subclasses which are equivalent to the full subcategories of injective and flat modules. Moreover, the authors investigate the question of when these subclasses form part of one of two classes of a cotorsion theory and other interesting results.

13C12 Torsion modules and ideals in commutative rings
13C11 Injective and flat modules and ideals in commutative rings
13D07 Homological functors on modules of commutative rings (Tor, Ext, etc.)
13D05 Homological dimension and commutative rings
Full Text: DOI