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- W2040693717 abstract "The concept of Faltings’ local-global principle for the minimaxness of local cohomology modules over a commutative Noetherian ring R is introduced, and it is shown that this principle holds at level 2. We also establish the same principle at all levels over an arbitrary commutative Noetherian ring of dimension not exceeding 3. These generalize the main results of Brodmann et al. in [6 Brodmann , M. P. , Rothaus , Ch. , Sharp , R. Y. ( 2000 ). On annihilators and associated primes of local cohomology modules . J. Pure and Appl. Algebra 153 : 197 – 227 .[Crossref], [Web of Science ®] , [Google Scholar]]. Moreover, it is shown that if M is a finitely generated R-module, bm𝔞 an ideal of R and r a non-negative integer such that is skinny for all i < r and for some positive integer t, then for any minimax submodule N of , the R-module is finitely generated. As a consequence, it follows that the associated primes of are finite. This generalizes the main results of Brodmann-Lashgari [5 Brodmann , M. P. , Lashgari , F. A. ( 2000 ). A finiteness result for associated primes of local cohomology modules . Proc. Amer. Math. Soc. 128 : 2851 – 2853 .[Crossref], [Web of Science ®] , [Google Scholar]] and Quy [16 Quy , P. H. ( 2010 ). On the finiteness of associated primes of local cohomology modules . Proc. Amer. Math. Soc. 138 : 1965 – 1968 .[Crossref], [Web of Science ®] , [Google Scholar]]." @default.
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- W2040693717 date "2014-08-13" @default.
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- W2040693717 title "Faltings' Local-Global Principle for the Minimaxness of Local Cohomology Modules" @default.
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- W2040693717 doi "https://doi.org/10.1080/00927872.2013.843094" @default.
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