Structure of Irreducible Homomorphisms to/from Free Modules

Saeed Nasseh; Ryo Takahashi

doi:10.1007/s10468-017-9722-z

Structure of Irreducible Homomorphisms to/from Free Modules

Saeed Nasseh, Ryo Takahashi

Mathematical Sciences

Nagoya University

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	471-485
Number of pages	15
Journal	Algebras and Representation Theory
Volume	21
Issue number	2
DOIs	https://doi.org/10.1007/s10468-017-9722-z
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

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10.1007/s10468-017-9722-z

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title = "Structure of Irreducible Homomorphisms to/from Free Modules",

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",

author = "Saeed Nasseh and Ryo Takahashi",

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AU - Nasseh, Saeed

AU - Takahashi, Ryo

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N2 - 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.

AB - 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.

KW - Auslander-Reiten conjecture

KW - Ext-vanishing

KW - Injective dimension

KW - Irreducible homomorphism

KW - Projective dimension

KW - Regular ring

KW - Tor-vanishing

UR - https://www.scopus.com/pages/publications/85023743737

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DO - 10.1007/s10468-017-9722-z

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EP - 485

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 2

ER -

Structure of Irreducible Homomorphisms to/from Free Modules

Abstract

Scopus Subject Areas

Keywords

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