Algebras and Representation Theory

, Volume 21, Issue 2, pp 471–485 | Cite as

Structure of Irreducible Homomorphisms to/from Free Modules

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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.

Keywords

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

Mathematics Subject Classification (2010)

13C10 13D05 13D07 13H05 

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Notes

Acknowledgments

We are grateful to the referee for reading the paper very carefully and for giving many valuable suggestions that improved the presentation of the paper significantly.

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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Mathematical SciencesGeorgia Southern UniversityStatesboroUSA
  2. 2.Graduate School of MathematicsNagoya UniversityAichiJapan

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