One-Dimensional Semilocal Cohen-Macaulay Rings

  • K. Kiyek
  • J. L. Vicente
Part of the Algebras and Applications book series (AA, volume 4)

Abstract

The local ring of a point on a curve is a one-dimensional local Cohen-Macaulay ring; in this chapter we study this class of rings. After proving some results on transversal elements in section 1, our main interest in section 2 is the integral closure of a one-dimensional local Cohen-Macaulay ring; we use Manis valuations in describing the integral closure. In section 3 we give necessary and sufficient conditions in order to ensure that the completion of a one-dimensional local Cohen-Macaulay ring which is a domain (resp. has no nilpotent elements) again is a domain (resp. has no nilpotent elements). Here the reader is supposed to be acquainted with the notion of the completion of a local ring and its properties.

Keywords

Alan Itan 

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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • K. Kiyek
    • 1
  • J. L. Vicente
    • 2
  1. 1.Department of MathematicsUniversity of PaderbornPaderbornGermany
  2. 2.Departamento de AlgebraUniversidad de SevillaSevillaSpain

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