Structure of Irreducible Homomorphisms to/from Free Modules
Algebras and Representation Theory
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.
Nasseh, Saeed, Ryo Takahashi.
"Structure of Irreducible Homomorphisms to/from Free Modules."
Algebras and Representation Theory: 1-15.