Commuting idempotents, square-free modules, and the exchange property.

DOI10.1016/j.jalgebra.2015.07.015zbMath1337.16008OpenAlexW1161458362MaRDI QIDQ745147

Pace P. Nielsen, Michał Ziembowski, Ryszard Mazurek

Publication date: 13 October 2015

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2015.07.015

zbMATH Keywords

direct sumsdirect summandsexchange ringsinternal exchange propertyfinite exchange propertylifting idempotents\(C_3\) propertycommuting idempotentshalf-commuting idempotentssquare-free modules

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) Generalizations of commutativity (associative rings and algebras) (16U80) Jacobson radical, quasimultiplication (16N20)

Related Items

D4-Modules, Perspectivity, exchange and summand-dual-square-free modules, Rings all of whose right ideals are U-modules, Utumi abelian groups, Direct complements almost unique, C4- and D4-Modules via perspective direct summands, C4-Modules, Dual-square-free modules, Utumi modules, An ensemble of idempotent lifting hypotheses, Dual Utumi modules, Rings whose Elements are the Sum of a Tripotent and an Element from the Jacobson Radical, N-chained semigroups and -perspective modules and rings, Rings whose cyclics are U-modules

Cites Work

• Strong lifting splits.
• Internal exchange property for square-free modules.
• Square-free modules with the exchange property.
• Exercises in classical ring theory.
• The exchange property of quasi-continuous modules with the finite exchange property
• Modules invariant under automorphisms of their covers and envelopes.
• Refinements for infinite direct decompositions of algebraic systems
• Decompositions of injective modules
• Exchange rings and decompositions of modules
• Countable Exchange and Full Exchange Rings
• Modules Whose Lattice of Submodules is Distributive
• Lifting Idempotents and Exchange Rings
• ABELIAN EXCHANGE MODULES
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