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Chain conditions in modules with krull dimension
Authors:Dilek Pusat-Yilmaz  Patrick F Smith
Institution:Department of Mathematics , University of Glasgow , Glasgow, Scotland, G12 8QW, UK
Abstract:Any ring with Krull dimension satisfies the ascending chain condition on semiprime ideals. This result does not hold more generally for modules. In particular if Ris the first Weyl algebra over a field of characteristic 0 then there are Artinian R-modules which do not satisfy the ascending chain condition on prime submodules. However, if Ris a ring which satisfies a polynomial identity then any R-module with Krull dimension satisfies the ascending chain condition on prime submodules, and, if Ris left Noethe-rian, also the ascending chain condition on semiprime submodules.
Keywords:
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