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.)
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© 2002 Springer Science+Business Media Dordrecht
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Tuganbaev, A. (2002). Exchange Rings and Modules. In: Rings Close to Regular. Mathematics and Its Applications, vol 545. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9878-1_6
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DOI: https://doi.org/10.1007/978-94-015-9878-1_6
Publisher Name: Springer, Dordrecht
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