Structure of irreducible homomorphisms to/from free modules

2016/06/08 by Nasseh, Saeed, Takahashi, Ryo
#13C10 #13D05 #13D07 #13H05 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.02621

Abstract

The primary goal of this paper is to investigate the structure of irreducible monomorphisms to and irreducible epimorphisms from finitely generated free modules over a noetherian local ring. Then we show that over such a ring, self-vanishing of Ext and Tor for a finitely generated module admitting such an irreducible homomorphism forces the ring to be regular.

Related

• Ascent of module structures, vanishing of Ext, and extended modules
• NAK for Ext and Ascent of module structures
• Finite homological dimension of Hom and vanishing of Ext
• Torsion-free Modules over Commutative Domains of Krull Dimension One
• Hom and Ext, Revisited