Brauer–Thrall for Totally Reflexive Modules over Local Rings of Higher Dimension
| Autor: | Ryo Takahashi, Olgur Celikbas, Mohsen Gheibi |
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| Rok vydání: | 2013 |
| Předmět: |
Noetherian
General Mathematics Local ring Multiplicity (mathematics) Commutative Algebra (math.AC) Mathematics - Commutative Algebra Combinatorics Residue field FOS: Mathematics Representation Theory (math.RT) Indecomposable module Commutative property Mathematics - Representation Theory Mathematics |
| Zdroj: | Algebras and Representation Theory. 17:997-1008 |
| ISSN: | 1572-9079 1386-923X |
| DOI: | 10.1007/s10468-013-9432-0 |
| Popis: | Let $R$ be a commutative Noetherian local ring. Assume that $R$ has a pair $\{x,y\}$ of exact zerodivisors such that $\dim R/(x,y)\ge2$ and all totally reflexive $R/(x)$-modules are free. We show that the first and second Brauer--Thrall type theorems hold for the category of totally reflexive $R$-modules. More precisely, we prove that, for infinitely many integers $n$, there exists an indecomposable totally reflexive $R$-module of multiplicity $n$. Moreover, if the residue field of $R$ is infinite, we prove that there exist infinitely many isomorphism classes of indecomposable totally reflexive $R$-modules of multiplicity $n$. to appear in Algebras and Representation Theory |
| Databáze: | OpenAIRE |
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