Kyoto J. Math. 55 (1), 169-185, (April 2015) DOI: 10.1215/21562261-2848151
Nguyen Tu Cuong, Shiro Goto, Nguyen Van Hoang
KEYWORDS: generalized local cohomology, $I$-cofiniteness, noetherian, 13D45, 13E99, 18G60
Let be a commutative Noetherian ring, let be an ideal of , and let , be two finitely generated -modules. The aim of this paper is to investigate the -cofiniteness of generalized local cohomology modules of and with respect to . We first prove that if is a principal ideal, then is -cofinite for all , and all . Secondly, let be a nonnegative integer such that for all . Then is -cofinite for all and is finitely generated. Finally, we show that if or , then is -cofinite for all .