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.
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© 2004 Springer Science+Business Media New York
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Kiyek, K., Vicente, J.L. (2004). One-Dimensional Semilocal Cohen-Macaulay Rings. In: Resolution of Curve and Surface Singularities. Algebras and Applications, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2029-2_2
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DOI: https://doi.org/10.1007/978-1-4020-2029-2_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6573-5
Online ISBN: 978-1-4020-2029-2
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