Weak Krull-Schmidt theorem and direct sum decompositions of serial modules of finite Goldie dimension.

DOI10.1016/J.JALGEBRA.2004.06.027zbMath1088.16008OpenAlexW2123723855MaRDI QIDQ706019

Pavel Příhoda

Publication date: 16 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.06.027

zbMATH Keywords

direct sumsuniserial modulesdirect summandsKrull-Schmidt theoremserial modulesfinite Goldie dimension

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 (7)

Weak Krull-Schmidt for infinite direct sums of cyclically presented modules over local rings. ⋮ Almost uniserial rings and modules. ⋮ Monogeny dimension relative to a fixed uniform module. ⋮ Direct-sum decompositions of modules with semilocal endomorphism rings ⋮ Direct summands of direct sums of modules whose endomorphism rings have two maximal right ideals. ⋮ On uniserial modules that are not quasi-small. ⋮ Endomorphism Rings with Finitely Many Maximal Right Ideals

Cites Work

• Unnamed Item
• Direct summands of serial modules
• Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
• Direct sum decompositions of modules, semilocal endomorphism rings, and Krull monoids
• \(K_0\) of a semilocal ring
• SOME MODEL THEORY OVER AN EXCEPTIONAL UNISERIAL RING AND DECOMPOSITIONS OF SERIAL MODULES

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