Exchange Rings and Modules

  • Askar Tuganbaev
Part of the Mathematics and Its Applications book series (MAIA, volume 545)


Let τ be a cardinal number. A module M is called a module with the τ-exchange property (see [123]) if for every module X and each direct decomposition X = M′⊕Y = ⊕ i∈I N i such that M′≌M and card(I) ≤ τ, there are submodules N i ⊆N i (i ∈ I) with X = M′⊕(⊕ i∈I N i ′. (It follows from the modular law that N i ′ must be a direct summand of N i for all i.)


Direct Summand Exchange Ring Exchange Module Invertible Element Regular Ring 
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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Askar Tuganbaev
    • 1
  1. 1.Moscow Power Engineering InstituteTechnological UniversityMoscowRussia

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