Asymptotic stability of primes associated to homogeneous components of multigraded modules

[摘要] Let A subset of B be a homogeneous extension of Noetherian standard N-r-graded rings with A(0) = B-0 = R. Let M be a finitely generated N-r-graded B-module and N subset of M a finitely generated graded A-submodule of M. In this paper, we investigate the asymptotic behavior of the set of primes associated to the module M-n/N-n and prove that for all sufficiently large n epsilon N-r, the set Ass(R)(M-n/N-n) is stable. We also give a certain inequality for the spread of standard multigraded rings, which is a natural generalization of Burch's inequality for the analytic spread of an ideal. (c) 2006 Published by Elsevier Inc.

[发布日期] 2006-12-15

[关键词] associated prime;multigraded;grade;spread