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Exchange Rings and Modules

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

Abstract

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.)

Keywords

Direct Summand Exchange Ring Exchange Module Invertible Element Regular Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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