MODULES HAVING VERY FEW ZERO-DIVISORS

Autor(en): Nasehpour, Peyman
Payrovi, Sh.
Stichwörter: Grade; Homological dimension; LOCAL COHOMOLOGY MODULES; Mathematics; ZD-modules
Erscheinungsdatum: 2010
Herausgeber: TAYLOR & FRANCIS INC
Journal: COMMUNICATIONS IN ALGEBRA
Volumen: 38
Ausgabe: 9
Startseite: 3154
Seitenende: 3162
Zusammenfassung: 
Let R be a commutative ring, I a finitely generated ideal of R, and M a zero-divisor R-module. It is shown that the M-grade of I defined by the Koszul complex is consistent with the definition of M-grade of I defined by the length of maximal M-sequences in I. Also, it is shown that, if R is Noetherian, then for any submodule N of M, the following conditions are equivalent: (1) Ass(R)(H(I)(0)(M/N)/L) is finite for all finitely generated submodules L of H(I)(0)(M/N); (2) If (H(I)(0)(M/N)/L), ... ,H(I)(i-1)(M/N) are finitely generated, then Ass(R)(H(I)(i)(M/N)/L) is finite for all finitely generated submodules L of H(I)(i)(M/N).
ISSN: 00927872
DOI: 10.1080/00927870903131098

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