Artinianess of Graded Generalized Local Cohomology Modules
محورهای موضوعی : Applied Mathematics
Sh. Tahamtan
1
(Department of Mathematics, Islamic Azad University, Borujerd-Branch, Borujerd, iran.)
کلید واژه: Artinian module, Generalized local cohomology module, Minimax module,
چکیده مقاله :
Let R = L n2N0Rn be a Noetherian homogeneous graded ring with local basering (R0;m0) of dimension d . Let R+ = Ln2NRn denote the irrelevant idealof R and let M and N be two nitely generated graded R-modules. Lett = tR+(M;N) be the rst integer i such that HiR+(M;N) is not minimax.We prove that if i t, then the set AssR0 (HiR+(M;N)n) is asymptoticallystable for n ! 1 and Hjm0 (HiR+(M;N)) is Artinian for 0 j 1. More-over, let s = sR+(M;N) be the largest integer i such that HiR+(M;N) is notminimax. For each i s, we prove that R0m0R0HiR+(M;N) is Artinian andthat Hjm0 (HiR+(M;N)) is Artinian for d 1 j d. Finally we show thatHd2m0 (HsR+(M;N)) is Artinian if and only if Hdm0 (Hs1R+(M;N)) is Artinian.
Let R = L n2N0Rn be a Noetherian homogeneous graded ring with local basering (R0;m0) of dimension d . Let R+ = Ln2NRn denote the irrelevant idealof R and let M and N be two nitely generated graded R-modules. Lett = tR+(M;N) be the rst integer i such that HiR+(M;N) is not minimax.We prove that if i t, then the set AssR0 (HiR+(M;N)n) is asymptoticallystable for n ! 1 and Hjm0 (HiR+(M;N)) is Artinian for 0 j 1. More-over, let s = sR+(M;N) be the largest integer i such that HiR+(M;N) is notminimax. For each i s, we prove that R0m0R0HiR+(M;N) is Artinian andthat Hjm0 (HiR+(M;N)) is Artinian for d 1 j d. Finally we show thatHd2m0 (HsR+(M;N)) is Artinian if and only if Hdm0 (Hs1R+(M;N)) is Artinian.
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