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Artinianness of Local Cohomology Modules Defined by a Pair of Ideals
Ist Teil von
Bulletin of the Malaysian Mathematical Sciences Society, 2012-01, Vol.35 (4)
Ort / Verlag
Heidelberg: Springer Nature B.V
Erscheinungsjahr
2012
Link zum Volltext
Quelle
EZB Electronic Journals Library
Beschreibungen/Notizen
Let ... be a commutative Noetherian ring and ..., ... two ideals of ... Let ... be a finitely generated ...-module; it is shown that (1) if ..., then ... is ...-cofinite Artinian for all ...; let ... (2) if ... is local and ... is a non-zero Serre subcategory of the category of ...-modules satisfying the condition ..., then ... ... (3) if ... has finite Krull dimension, then ... Furthermore, notion of ...-relative Goldie dimension of modules is defined and it is shown that ... is Artinian, whenever ... is a ...-module of dimension ... such that the ...-relative Goldie dimension of any quotient of ... is finite. 2010 Mathematics Subject Classification: 13D45, 14B15, 13E10. (ProQuest: ... denotes formulae omitted.)