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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geprüft am 29.05.2024