Criteria for flatness and injectivity

Autor(en): Epstein, Neil
Yao, Yongwei
Stichwörter: ARTINIAN-MODULES; Associated prime; Coassociated prime; DECOMPOSITION; DIMENSION; Divisible module; Flat module; h-divisible module; HOMOLOGY; Injective module; Mathematics; NOETHERIAN-RINGS; PRIMES; Torsion-free module
Erscheinungsdatum: 2012
Herausgeber: SPRINGER
Journal: MATHEMATISCHE ZEITSCHRIFT
Volumen: 271
Ausgabe: 3-4
Startseite: 1193
Seitenende: 1210
Zusammenfassung: 
Let R be a commutative Noetherian ring. We give criteria for flatness of R-modules in terms of associated primes and torsion-freeness of certain tensor products. This allows us to develop a criterion for regularity if R has characteristic p, or more generally if it has a locally contracting endomorphism. Dualizing, we give criteria for injectivity of R-modules in terms of coassociated primes and (h-)divisibility of certain Hom-modules. Along the way, we develop tools to achieve such a dual result. These include a careful analysis of the notions of divisibility and h-divisibility (including a localization result), a theorem on coassociated primes across a Hom-module base change, and a local criterion for injectivity.
ISSN: 00255874
DOI: 10.1007/s00209-011-0910-y

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