A criterion for dualizing modules

2015/03/14 by Kamran Divaani-Aazar, Divaani-Aazar, Kamran, Massoumeh Nikkhah Babaei +3
Mathematics · #13C05 #13D07 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C05 #msc:13D07 #msc:13H10

paper · pdf · doi:10.48550/arxiv.1503.04295

To appear in Tokyo journal of Mathematics

arxiv created 2015/03/14 · arxiv updated 2015/03/17

Abstract

We establish a characterization of dualizing modules among semidualizing modules. Let R be a finite dimensional commutative Noetherian ring with identity and C a semidualizing R-module. We show that C is a dualizing R-module if and only if Tor_i^R(E,E') is C- injective for all C-injective R-modules E and E' and all i≥ 0.

Related

• Some new Subcategories and homological dimensions related to Semidualizing modules
• Dual of Bass numbers and dualizing modules
• Tensor Product of C-Injective Modules
• Presentations of rings with non-trivial semidualizing modules
• Semi-dualizing modules and related Gorenstein homological dimensions