caa a22 4500 606161163 CHVBK 20210128100633.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10468-014-9498-3 doi (NATIONALLICENCE)springer-10.1007/s10468-014-9498-3 Cofiniteness with Respect to Ideals of Small Dimensions [Elektronische Daten] [Kamal Bahmanpour, Reza Naghipour, Monireh Sedghi] Let R be a Noetherian ring, I an ideal of R and M an R-module. It is shown that if Ext R i ( R / I , M ) ${\operatorname {Ext}^{i}_{R}}(R/I,M)$ is finitely generated, for all i≤ dimM, then Ext R i ( N , M ) ${\operatorname {Ext}^{i}_{R}}(N, M)$ is finitely generated for all i≥0 and all finitely generated R-modules N with Supp N⊆V(I) and dim N≤1. In addition, we show that if R is local, then Ext R i ( N , M ) ${\operatorname {Ext}^{i}_{R}}(N, M)$ is finitely generated for each i≥0 and for each finitely generated R-module N with Supp N⊆V(I) and dim N≤2. As a consequence we deduce that if dim R/I=2 and Supp M⊆V(I), then M is I-cofinite if (and only if) HomR(R/I,M), Ext R 1 ( R / I , M ) ${\operatorname {Ext}^{1}_{R}}(R/I,M)$ and Ext R 2 ( R / I , M ) ${\operatorname {Ext}^{2}_{R}}(R/I,M)$ are finitely generated. These generalize the main results of Melkersson [(J. Algebra. 372, 459-462, 2012) Theorem 2.3] and Bahmanpour et al. [(Proc. Amer. Math. Soc. 142, 1101-1107, 2014) Proposition 2.6]. Springer Science+Business Media Dordrecht, 2014 Cofinite modules nationallicence Bass numbers nationallicence Local cohomology nationallicence Bahmanpour Kamal Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran aut Naghipour Reza Department of Mathematics, University of Tabriz, Tabriz, Iran aut Sedghi Monireh Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran aut Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 369-379 1386-923X 18:2<369 2015 18 10468 https://doi.org/10.1007/s10468-014-9498-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-014-9498-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bahmanpour Kamal Department of Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran aut NATIONALLICENCE 700 1- Naghipour Reza Department of Mathematics, University of Tabriz, Tabriz, Iran aut NATIONALLICENCE 700 1- Sedghi Monireh Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 369-379 1386-923X 18:2<369 2015 18 10468