Reduction of Ideals Relative to an Artinian Module and the Dual of Burch,s Inequality  

作　　者：Fatemeh Cheraghi Amir Mafi 

机构地区：[1]Department of Mathematics, University of Kurdistan, P.O. Box: 416, Sanandaj, Iran

出　　处：《Algebra Colloquium》2019年第1期113-122,共10页代数集刊（英文版）

摘　　要：Let (A,m) be a commutative quasi-local ring with non-zero identity and M be an Artinian A-module with dim M = d. If I is an ideal of A with l(0 :m I)<∞, then we show that for a minimal reduction J of I,(0 : m JI)=(0 :m I^2) if and only if l(0:M I^n+1)=l(0:m J)^(n+d/d)-l(0 :M J)/(0 :M I))(n+d-1/d-1) for all n≥> 0. Moreover, we study the dual of Burch's inequality. In particular, the Burch's inequality becomes an equality if G(I,M) is co-Cohen-Macaulay.

关 键 词：REDUCTION of IDEALS ARTINIAN MODULES co-Cohen-Macaulay 

分 类 号：TP393.06[自动化与计算机技术—计算机应用技术]