Cofiniteness with respect to ideals of dimension one
2012 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 372, 459-462 p.Article in journal (Refereed) Published
We prove that the category of modules cofinite with respect to an ideal of dimension one in a noetherian ring is a full abelian subcategory of the category of modules. The proof is based on a criterion for cofiniteness with respect to an ideal of dimension one. Namely for such ideals it suffices that the two first Ext-modules in the definition for cofiniteness are finitely generated. This criterion is also used to prove very simply that all local cohomology modules of a finitely generated module with respect to an ideal of dimension one in an arbitrary noetherian ring are cofinite with respect to the ideal.
Place, publisher, year, edition, pages
Elsevier , 2012. Vol. 372, 459-462 p.
Cofinite module, Local cohomology module
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-86368DOI: 10.1016/j.jalgebra.2012.10.005ISI: 000311187200023OAI: oai:DiVA.org:liu-86368DiVA: diva2:576911