Chi tiết| Tên | On the cofiniteness of generalized local cohomology modules (SCIE) |
| Lĩnh vực | Toán học |
| Tác giả | Nguyen Tu Cuong, Shiro Goto, Nguyen Van Hoang |
| Nhà xuất bản / Tạp chí | Kyoto Journal of Mathematics (SCIE) Năm 2015 |
| Số hiệu ISSN/ISBN | |
| Tóm tắt nội dung | |
Let R be a commutative Noetherian ring, I an ideal of R and M, N two finitely generated R-modules. The aim of this paper is to investigate the I-co niteness of generalized local cohomology modules H^j_I(M;N) of M and N with respect to I. We fi rst prove that if I is a principal ideal then H^j_I(M;N) is I-co finite for all M;N and all j. Secondly, let t be a non-negative integer such that \dim\Supp(H^j_I(M;N))<=1 for all j < t. Then H^j_I(M;N) is I-co finite for all j < t and Hom(R/I;H^t_I(M;N)) is finitely generated. Finally, we show that if \dim(M)<= 2 or \dim(N) <= 2 then H^j_I(M;N) is I-cofi nite for all j.
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