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Relative (co)homology of \(F\)-Gorenstein modules. (English) Zbl 1373.16027

Summary: We investigate the relative cohomology and relative homology theories of \(F\)-Gorenstein modules, consider the relations between classical and \(F\)-Gorenstein (co)homology theories.

MSC:

16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
18G25 Relative homological algebra, projective classes (category-theoretic aspects)
13D05 Homological dimension and commutative rings
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