Fitting ideals and the Gorenstein property

2009/02/18 by Burcu Baran, Baran, Burcu
Mathematics · #13C40 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C40

paper · pdf · doi:10.48550/arxiv.0902.3204

9 pages

arxiv created 2009/10/14 · arxiv updated 2009/12/01

Abstract

Let p be a prime number and G be a finite commutative group such that p² does not divide the order of G. In this note we prove that for every finite module M over the group ring Z_p[G], the inequality #M ≤ #Z_p[G]/Fit_Z_p[G](M) holds. Here, Fit_Z_p[G](M) is the Z_p[G]-Fitting ideal of M.

Related

• Notes on noncommutative Fitting invariants
• Ideals and their Fitting ideals
• Testing for the Gorenstein property
• A Fitting Lemma for Z/2-graded modules
• The reduction number of canonical ideals