A Version of the Weak Krull–Schmidt Theorem for Infinite Direct Sums of Uniserial Modules

DOI10.1080/00927870500455049zbMath1098.16004OpenAlexW2101356924MaRDI QIDQ5470006

Pavel Příhoda

Publication date: 29 May 2006

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

Full work available at URL: https://doi.org/10.1080/00927870500455049

zbMATH Keywords

direct sumsuniserial modulesdirect summandsweak Krull-Schmidt theoremquasismall modulesepigeny classesmonogeny classes

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)

Related Items (8)

Weak Krull-Schmidt for infinite direct sums of cyclically presented modules over local rings. ⋮ Projective modules are determined by their radical factors. ⋮ Almost uniserial rings and modules. ⋮ Monogeny dimension relative to a fixed uniform module. ⋮ DIRECT SUMS OF INFINITELY MANY KERNELS ⋮ The Infinite Krull–Schmidt Property in the Case 2 ⋮ Direct-sum decompositions of modules with semilocal endomorphism rings ⋮ Direct products of modules whose endomorphism rings have at most two maximal ideals

Cites Work

• Weak Krull-Schmidt for infinite direct sums of uniserial modules
• Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
• SOME MODEL THEORY OVER AN EXCEPTIONAL UNISERIAL RING AND DECOMPOSITIONS OF SERIAL MODULES

This page was built for publication: A Version of the Weak Krull–Schmidt Theorem for Infinite Direct Sums of Uniserial Modules