Covariant functors and asymptotic stability

JOURNAL OF ALGEBRA

卷:484

Article

Se, Tony^1,2 

[1] Univ Kansas, Dept Math, 405 Snow Hall,1460 Jayhawk Blvd, Lawrence, KS 66045 USA

[2] Univ Mississippi, Dept Math, 305 Hume Hall, University, MS 38677 USA

关键词: Associated prime;    Coherent functor;   

DOI  :  10.1016/j.jalgebra.2017.04.009

来源: Elsevier

【 摘 要 】

Let R be a commutative Noetherian ring, I, J ideals of R and M a finitely generated R-module. Let F be a covariant R-linear functor from the category of finitely generated R-modules to itself. We first show that if F is coherent, then the sets Ass(R) F(M/(IM)-M-n), Ass(R) F(In-1M/(IM)-M-n) and the values depth(J) F(M/(IM)-M-n), depth(J) F(In-1M/(IM)-M-n) become independent of n for large n. Next, we consider several examples in which F is a rather familiar functor, but is not coherent or not even finitely generated in general. In these cases, the sets AssR F(M/(IM)-M-n) still become independent of n for large n. We then show one negative result where F is not finitely generated. Finally, we give a positive result where F belongs to a special class of functors which are not finitely generated in general, an example of which is the zeroth local cohomology functor. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free