Coherent functors and asymptotic stability

JOURNAL OF ALGEBRA

卷:522

Article

Banda, Adson¹  Melkersson, Leif² 

[1] Univ Zambia, Dept Math & Stat, Lusaka, Zambia

[2] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

关键词: Asymptotic prime ideal;    Coherent functor;    Hilbert polynomial;    Betti number;    Bass number;   

DOI  :  10.1016/j.jalgebra.2018.11.035

来源: Elsevier

【 摘 要 】

Asymptotic properties of high powers of an ideal related to a coherent functor F are investigated. It is shown that when N is an artinian module the sets of attached prime ideals Att(A) F(0 :(N) a(n)) are the same for n large enough. Also it is shown that for an artinian module N if the modules F(0 :(N) a(n)) have finite length and for a finitely generated module M if the modules F(M/a(n) M) have finite length, their lengths are given by polynomials in n, for large n. When A is local it is shown that, the Betti numbers beta(i)(F(M /a(n) M)) and the Bass numbers mu(i)(F(M / a(n) M)) are given by polynomials in n for large n. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free