Open Access
Translator Disclaimer
WINTER 2013 Indecomposable injective modules of finite Malcev rank over local commutative rings
François Couchot
J. Commut. Algebra 5(4): 481-505 (WINTER 2013). DOI: 10.1216/JCA-2013-5-4-481

Abstract

It is proven that each indecomposable injective module over a valuation domain $R$ is polyserial if and only if each maximal immediate extension $\widehat{R}$ of $R$ is of finite rank over the completion $\widetilde{R}$ of $R$ in the $R$-topology. In this case, for each indecomposable injective module $E$, the following invariants are finite and equal: its Malcev rank, its Fleischer rank and its dual Goldie dimension. Similar results are obtained for chain rings satisfying some additional properties. It is also shown that each indecomposable injective module over local Noetherian rings of Krull dimension one has finite Malcev rank. The preservation of the finiteness of Goldie dimension by localization is investigated too.

Citation

Download Citation

François Couchot. "Indecomposable injective modules of finite Malcev rank over local commutative rings." J. Commut. Algebra 5 (4) 481 - 505, WINTER 2013. https://doi.org/10.1216/JCA-2013-5-4-481

Information

Published: WINTER 2013
First available in Project Euclid: 31 January 2014

zbMATH: 1291.13037
MathSciNet: MR3161743
Digital Object Identifier: 10.1216/JCA-2013-5-4-481

Subjects:
Primary: 13C11 , 13E05 , 13F30

Keywords: Chain ring , Goldie dimension , indecomposable injective module , polyserial module , Valuation domain

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
25 PAGES


SHARE
Vol.5 • No. 4 • WINTER 2013
Back to Top