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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. © 2010 Elsevier Ltd.

Registro:

Documento: Artículo
Título:Normalization of rings
Autor:Greuel, G.-M.; Laplagne, S.; Seelisch, F.
Filiación:Department of Mathematics, University of Kaiserslautern, P.O. Box 3049, Kaiserslautern 67653, Germany
Departamento de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria - Pabellón I, (C1428EGA) Buenos Aires, Argentina
Palabras clave:Grauert-Remmert criterion; Integral closure; Normalization; Test ideal
Año:2010
Volumen:45
Número:9
Página de inicio:887
Página de fin:901
DOI: http://dx.doi.org/10.1016/j.jsc.2010.04.002
Título revista:Journal of Symbolic Computation
Título revista abreviado:J. Symb. Comput.
ISSN:07477171
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_07477171_v45_n9_p887_Greuel.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v45_n9_p887_Greuel

Referencias:

  • Bosma, W., Cannon, J.J., Playoust, C., The Magma algebra system. I. The user language (1997) J. Symbolic Comput., 24 (3-4), pp. 235-265
  • Brennan, J.P., Vasconcelos, W.V., On the structure of closed ideals (2001) Math. Scand., 88 (1), pp. 3-16
  • Bruns, W., Koch, R., Computing the integral closure of an affine semigroup (2001) Univ. Iagel. Acta Math., 39, pp. 59-70
  • Campillo, A., Greuel, G.-M., Lossen, C., Equisingular calculations for plane curve singularities (2007) J. Symbolic Comput., 42, pp. 89-114
  • Cohen, H., A course in computational algebraic number theory (1993) Graduate Texts in Mathematics, 138. , Springer-Verlag, Berlin
  • de Jong, T., An algorithm for computing the integral closure (1998) J. Symbolic Comput., 26 (3), pp. 273-277
  • Decker, W., de Jong, T., Greuel, G.-M., Pfister, G., The normalization: a new algorithm, implementation and comparisons (1999) Progr. Math., 173, pp. 177-185. , Birkhäuser, Basel, Computational Methods for Representations of Groups and Algebras (Essen, 1997)
  • Ford, D.J., The construction of maximal orders over a Dedekind domain (1987) J. Symbolic Comput., 4 (1), pp. 69-75
  • Gianni, P., Trager, B., Integral closure of Noetherian rings (1997) Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation, pp. 212-216. , ACM, New York, (electronic)
  • Grauert, H., Remmert, R., (1971) Analytische Stellenalgebren, , Springer-Verlag, Berlin, (unter Mitarbeit von O. Riemenschneider, Die Grundlehren der mathematischen Wissenschaften, Band 176)
  • Grayson, D.R., Stillman, M.E., (2009), http://www.math.uiuc.edu/Macaulay2/, Macaulay2 1.2, a software system for research in algebraic geometry. Available at:; Greuel, G.-M., Laplagne, S., Pfister, G., (2009), a. normal.lib, a Singular library for computing the normalization of affine rings; Greuel, G.-M., Pfister, G., Schönemann, H., (2009), http://www.singular.uni-kl.de, b). Singular 3.1.0 - A computer algebra system for polynomial computations; Greuel, G.-M., Pfister, G., (2008) A Singular Introduction to Commutative Algebra, , Springer, Berlin, (with contributions by Olaf Bachmann, Christoph Lossen and Hans Schönemann, With 1 CD-ROM (Windows, Macintosh and UNIX))
  • Leonard, D.A., Pellikaan, R., Integral closures and weight functions over finite fields (2003) Finite Fields Appl., 9 (4), pp. 479-504
  • Matsumoto, R., Computing the radical of an ideal in positive characteristic (2001) J. Symbolic Comput., 32 (3), pp. 263-271
  • Seidenberg, A., Construction of the integral closure of a finite integral domain (1970) Rend. Sem. Mat. Fis. Milano, 40, pp. 100-120
  • Seidenberg, A., Construction of the integral closure of a finite integral domain. II (1975) Proc. Amer. Math. Soc., 52, pp. 368-372
  • Singh, A., Swanson, I., (2008), arxiv://arxiv.org/abs/0901.0871, An algorithm for computing the integral closure. Preprint available at arXiv:; Stolzenberg, G., Constructive normalization of an algebraic variety (1968) Bull. Amer. Math. Soc., 74, pp. 595-599
  • Swanson, I., Huneke, C., Integral closure of ideals, rings, and modules (2006) London Mathematical Society Lecture Note Series, 336. , Cambridge University Press, Cambridge
  • Traverso, C., (1986), A study on algebraic algorithms: the normalization. Rend. Sem. Mat. Univ. Politec. Torino (Special Issue), 111-130 (1987), conference on algebraic varieties of small dimension (Turin, 1985); Vasconcelos, W., Integral closure (2005) Springer Monographs in Mathematics, , Springer-Verlag, Berlin, Rees Algebras, Multiplicities, Algorithms
  • Vasconcelos, W.V., Computing the integral closure of an affine domain (1991) Proc. Amer. Math. Soc., 113 (3), pp. 633-638
  • Vasconcelos, W.V., Computational methods in commutative algebra and algebraic geometry (1998) Algorithms and Computation in Mathematics, 2. , Springer-Verlag, Berlin, (with chapters by David Eisenbud, Daniel R. Grayson, Jürgen Herzog and Michael Stillman)
  • Vasconcelos, W.V., Divisorial extensions and the computation of integral closures (2000) J. Symbolic Comput., 30 (5), pp. 595-604

Citas:

---------- APA ----------
Greuel, G.-M., Laplagne, S. & Seelisch, F. (2010) . Normalization of rings. Journal of Symbolic Computation, 45(9), 887-901.
http://dx.doi.org/10.1016/j.jsc.2010.04.002
---------- CHICAGO ----------
Greuel, G.-M., Laplagne, S., Seelisch, F. "Normalization of rings" . Journal of Symbolic Computation 45, no. 9 (2010) : 887-901.
http://dx.doi.org/10.1016/j.jsc.2010.04.002
---------- MLA ----------
Greuel, G.-M., Laplagne, S., Seelisch, F. "Normalization of rings" . Journal of Symbolic Computation, vol. 45, no. 9, 2010, pp. 887-901.
http://dx.doi.org/10.1016/j.jsc.2010.04.002
---------- VANCOUVER ----------
Greuel, G.-M., Laplagne, S., Seelisch, F. Normalization of rings. J. Symb. Comput. 2010;45(9):887-901.
http://dx.doi.org/10.1016/j.jsc.2010.04.002