Structure of Irreducible Homomorphisms to/from Free Modules

Saeed Nasseh, Ryo Takahashi

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageEnglish
Pages (from-to)471-485
Number of pages15
JournalAlgebras and Representation Theory
Volume21
Issue number2
DOIs
StatePublished - Apr 1 2018

Scopus Subject Areas

  • General Mathematics

Keywords

  • Auslander-Reiten conjecture
  • Ext-vanishing
  • Injective dimension
  • Irreducible homomorphism
  • Projective dimension
  • Regular ring
  • Tor-vanishing

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