On uniserial modules that are not quasi-small.

DOI10.1016/j.jalgebra.2005.11.010zbMath1103.16005OpenAlexW2113098757MaRDI QIDQ2497460

Pavel Příhoda

Publication date: 4 August 2006

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2005.11.010

zbMATH Keywords

direct sumsuniserial modulesdirect summandsKrull-Schmidt theoremserial modulespure-projective modulesquasi-small modules

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) 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

Pure projective modules over chain domains with Krull dimension, Projective modules are determined by their radical factors., The isomorphism problem for uniserial modules over an arbitrary ring, The Infinite Krull–Schmidt Property in the Case 2, An indecomposable direct summand of a serial module which is not uniserial, Pure projective modules over non-singular serial rings

Cites Work

• Weak Krull-Schmidt theorem and direct sum decompositions of serial modules of finite Goldie dimension.
• Global Azumaya theorems in additive categories
• Direct summands of serial modules
• Weak Krull-Schmidt for infinite direct sums of uniserial modules
• Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
• Projective modules over the endomorphism ring of a biuniform module.
• SOME MODEL THEORY OVER AN EXCEPTIONAL UNISERIAL RING AND DECOMPOSITIONS OF SERIAL MODULES
• Some model theory over a nearly simple uniserial domain and decompositions of serial modules