Gorenstein injective dimension and a generalization of Ischebeck Formula

2011/05/12 by Reza Sazeedeh, Sazeedeh, Reza
Mathematics · #13D05 #13D07 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D05 #msc:13D07 #msc:13H10

paper · pdf · doi:10.48550/arxiv.1105.2399

5 pages

arxiv created 2011/05/12 · arxiv updated 2011/05/13

Abstract

Let (R,\frak m) be a commutative Noetherian local ring and let M and N be finitely generated R-modules of finite injective dimension and finite Gorenstein injective dimension, respectively. In this paper we prove a generalization of Ischebeck Formula, that is \depth_RM+sup\i| 0.1cm\Ext_Rⁱ(M,N)≠ 0\=\depth R.

Related

• Gorenstein injective dimension, Bass formula and Gorenstein rings
• A Bass equality for Gorenstein injective dimension of modules finite over homomorphisms
• Transfer of Gorenstein dimensions along ring homomorphisms
• Gorenstein dimension of modules over homomorphisms
• Ischebeck's formula, grade and quasi-homological dimensions