Syzygy modules with semidualizing or G-projective summands

DOI10.1016/j.jalgebra.2005.01.012zbMath1111.13015arXivmath/0501342OpenAlexW2027264989MaRDI QIDQ2576980

Ryo Takahashi

Publication date: 29 December 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0501342

zbMATH Keywords

syzygiessemidualizing moduleGorenstein dimension

Mathematics Subject Classification ID

Syzygies, resolutions, complexes and commutative rings (13D02)

Related Items (20)

Trace ideals of semidualizing modules and two generalizations of nearly Gorenstein rings ⋮ Characterizations of regular local rings via syzygy modules of the residue field ⋮ The trace property in preenveloping classes ⋮ Totally reflexive modules and Poincaré series ⋮ WeaklyG_K-Perfect and Integral Closure of Ideals ⋮ Intersections of resolving subcategories and intersections of thick subcategories ⋮ The transpose of modules relative to subcategories ⋮ Unnamed Item ⋮ Gorenstein rings via homological dimensions, and symmetry in vanishing of Ext and Tate cohomology ⋮ Some criteria for regular and Gorenstein local rings via syzygy modules ⋮ New Characterizations of Dualizing Modules ⋮ Modules of infinite regularity over commutative graded rings ⋮ Structure of irreducible homomorphisms to/from free modules ⋮ Free summands of syzygies of modules over local rings ⋮ Generation in singularity categories of hypersurfaces of countable representation type ⋮ Associated primes and syzygies of linked modules ⋮ Residually faithful modules and the Cohen-Macaulay type of idealizations ⋮ VANISHING OF (CO)HOMOLOGY OVER DEFORMATIONS OF COHEN-MACAULAY LOCAL RINGS OF MINIMAL MULTIPLICITY ⋮ On delta invariants and indices of ideals ⋮ On the subcategories of \(n\)-torsionfree modules and related modules

Cites Work

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• Gorenstein dimensions
• Gorenstein injective and projective modules
• Liftings and weak liftings of modules
• Semi-dualizing complexes and their Auslander categories
• Gorenstein dimension and torsion of modules over commutative noetherian rings
• Gorenstein Modules and Related Modules.
• Direct Summands of Syzygy Modules of the Residue Class Field
• Stable module theory

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