Normalization of rings

Authors:
Gert-Martin Greuel;Santiago Laplagne;Frank Seelisch
Affiliations:
Department of Mathematics, University of Kaiserslautern, P.O. Box 3049, (67653) Kaiserslautern, Germany;Departamento de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I - (C1428EGA), Buenos Aires, Argentina;Department of Mathematics, University of Kaiserslautern, P.O. Box 3049, (67653) Kaiserslautern, Germany
Venue:
Journal of Symbolic Computation
Year:
2010

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Abstract

We present a new algorithm to compute the integral closure of a reduced Noetherian ring in its total ring of fractions. A modification, applicable in positive characteristic, where actually all computations are over the original ring, is also described. The new algorithm of this paper has been implemented in Singular, for localizations of affine rings with respect to arbitrary monomial orderings. Benchmark tests show that it is in general much faster than any other implementation of normalization algorithms known to us.