A FORMULA FOR REDUCTION NUMBER OF AN IDEAL RELATIVE TO A NOETHERIAN MODULE

Authors : Naser ZAMANİ

Pages : 114-120

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Publication Date : 2009-06-01

Article Type : Research Paper

Abstract :Let insert ignore into journalissuearticles values(A, m); be a Noetherian local ring with infinite residue field and E be a finitely generated d dimensional Cohen-Macaulay A-module. Let b be an ideal of A such that htEb = 0 and λinsert ignore into journalissuearticles values(b, E); = 1. Assume that bp = 0 for all p ∈ Mininsert ignore into journalissuearticles values(E/bE);. Let rinsert ignore into journalissuearticles values(b, E); > 0. We show that if Gbinsert ignore into journalissuearticles values(E); is Cohen-Macaulay, then rinsert ignore into journalissuearticles values(b, E); = ainsert ignore into journalissuearticles values(Gbinsert ignore into journalissuearticles values(E);); + 1.
Keywords : associated graded rings and modules, graded local cohomology, reduction number and analytic spread of an ideal relative to a module