Square-free modules with the exchange property.

DOI10.1016/j.jalgebra.2009.12.035zbMath1213.16003OpenAlexW2045107304MaRDI QIDQ965182

Pace P. Nielsen

Publication date: 21 April 2010

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2009.12.035

zbMATH Keywords

direct sumsdirect summandsexchange ringsAbelian ringsfinite exchange propertysquare-free modulesfull exchange propertyleft linear Hausdorff topologies

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) Topological and ordered rings and modules (16W80) General module theory in associative algebras (16D10)

Related Items (14)

D4-Modules ⋮ C4-modules with the exchange property ⋮ Perspectivity, exchange and summand-dual-square-free modules ⋮ Utumi abelian groups ⋮ Direct complements almost unique ⋮ Automorphism-invariant modules satisfy the exchange property. ⋮ Unnamed Item ⋮ C4-Modules ⋮ Dual-square-free modules ⋮ AB5*-modules with the exchange property ⋮ Utumi modules ⋮ Half-orthogonal sets of idempotents ⋮ Commuting idempotents, square-free modules, and the exchange property. ⋮ Modules invariant under automorphisms of their covers and envelopes.

Cites Work

• Classes of modules with the exchange property
• Exchange Leavitt path algebras and stable rank
• On rings whose projective modules have the exchange property
• Separative cancellation for projective modules over exchange rings
• Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
• Rings and modules with exchange properties
• Strong lifting.
• The exchange property of quasi-continuous modules with the finite exchange property
• Refinements for infinite direct decompositions of algebraic systems
• Semi-commutativity and the McCoy condition.
• Exchange rings and decompositions of modules
• Countable Exchange and Full Exchange Rings
• Lifting Idempotents and Exchange Rings
• On modules for which the finite exchange property implies the countable exchange property
• A CRASH COURSE ON STABLE RANGE, CANCELLATION, SUBSTITUTION AND EXCHANGE
• ABELIAN EXCHANGE MODULES
• Endomorphism Rings of Projective Modules
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