A Krull-Schmidt theorem for Noetherian modules

DOI10.1006/jabr.2002.9142zbMath1005.16023OpenAlexW1976976927MaRDI QIDQ1614643

Gary Brookfield

Publication date: 8 September 2002

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2002.9142

zbMATH Keywords

Krull-Schmidt theoremNoetherian modulesFitting's lemmalocal endomorphism ringsdirect sums of indecomposable modulesdirect sum cancellationordinal lengths

Mathematics Subject Classification ID

Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Noetherian rings and modules (associative rings and algebras) (16P40)

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Unnamed Item ⋮ Direct-sum decompositions of modules with semilocal endomorphism rings ⋮ The theory of ordinal length

Cites Work

• A theory of length for Noetherian modules
• Krull-Schmidt uniqueness fails dramatically over subrings of Z\(\oplus\dots \oplus Z\)
• Cancellation and direct summands in dimension 1
• Direct sum cancellation of Noetherian modules
• THE LENGTH OF NOETHERIAN MODULES
• On semilocal rings
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