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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.

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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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Authors and Affiliations

  1. Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460, USA

    Saeed Nasseh

  2. Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, Aichi, 464-8602, Japan

    Ryo Takahashi

Authors
  1. Saeed Nasseh
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  2. Ryo Takahashi
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Corresponding author

Correspondence to Saeed Nasseh.

Additional information

Presented by Steffen Koenig.

Takahashi was partly supported by JSPS Grants-in-Aid for Scientific Research 16K05098.

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Nasseh, S., Takahashi, R. Structure of Irreducible Homomorphisms to/from Free Modules. Algebr Represent Theor 21, 471–485 (2018). https://doi.org/10.1007/s10468-017-9722-z

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