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Certain Chain Conditions in Modules over Dedekind Domains and Related Rings

  • Esperanza Sanchez Campos
  • Patrick F. Smith
Part of the Trends in Mathematics book series (TM)

Abstract

Necessary and sufficient conditions are given for a module over a Dedekind domain to satisfy the ascending chain condition on n-generated submodules for every positive integer n or on submodules with uniform dimension at most n for every positive integer n. These results are then extended to modules over commutative Noetherian domains which need not be Dedekind.

Keywords

Chain conditions Dedekind domain Uniform dimension 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Esperanza Sanchez Campos
    • 1
  • Patrick F. Smith
    • 2
  1. 1.Departamento de Álgebra, Geometría y TopologíaUniversidad de MálagaMálagaSpain
  2. 2.Department of MathematicsUniversity of GlasgowGlasgow, ScotlandUK

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