Faltings’ local–global principle for the in dimension < n of local cohomology modules

• Published in: Communications in algebra Vol. 46; no. 8; pp. 3496 - 3509
• Main Authors: Naghipour, Reza, Maddahali, Robabeh, Ahmadi Amoli, Khadijeh
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Ltd 03.08.2018
• Subjects: Minimax technique; Modules
• ISSN: 0092-7872; 1532-4125
• DOI: 10.1080/00927872.2017.1412453

The concept of Faltings' local-global principle for the in dimension <n of local cohomology modules over a Noetherian ring R is introduced, and it is shown that this principle holds at levels 1, 2. We also establish the same principle at all levels over an arbitrary Noetherian ring of dimension not exceeding 3. These generalize the main results of Brodmann et al. [8]. Moreover, as a generalization of Raghavan's result, we show that the Faltings' local-global principle for the in dimension <n of local cohomology modules holds at all levels r[element of]N whenever the ring R is a homomorphic image of a Noetherian Gorenstein ring. Finally, it is shown that if M is a finitely generated R-module, [MATHEMATICAL FRAKTUR SMALL A] an ideal of R and r a non-negative integer such that [Formula omitted.] is in dimension < 2 for all i<r and for some positive integer t, then for any minimax submodule N of [Formula omitted.] , the R-module [Formula omitted.] is finitely generated. As a consequence, it follows that the associated primes of [Formula omitted.] are finite. This generalizes the main results of Brodmann-Lashgari [7] and Quy [24].