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.
Original language | English |
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Pages (from-to) | 471-485 |
Number of pages | 15 |
Journal | Algebras and Representation Theory |
Volume | 21 |
Issue number | 2 |
DOIs | |
State | Published - Apr 1 2018 |
Scopus Subject Areas
- General Mathematics
Keywords
- Auslander-Reiten conjecture
- Ext-vanishing
- Injective dimension
- Irreducible homomorphism
- Projective dimension
- Regular ring
- Tor-vanishing