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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A simple algorithm for principalization of monomial ideals
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by Russell A. Goward Jr. PDF
Trans. Amer. Math. Soc. 357 (2005), 4805-4812 Request permission

Abstract:

In this paper, we give a simple constructive proof of principalization of monomial ideals and the global analog. This also gives an algorithm for principalization.
References
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  • Santiago Encinas and Orlando Villamayor, A course on constructive desingularization and equivariance, Resolution of singularities (Obergurgl, 1997) Progr. Math., vol. 181, Birkhäuser, Basel, 2000, pp. 147–227. MR 1748620
  • Goward, Russell, A., A Principalizing Ideal of a Monomial Ideal, preprint.
  • Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
  • Heisuke Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109–203; ibid. (2) 79 (1964), 205–326. MR 0199184, DOI 10.2307/1970547
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Additional Information
  • Russell A. Goward Jr.
  • Affiliation: Department of Mathematics, University of Michigan-Ann Arbor, Ann Arbor, Michigan 48109-1109
  • Received by editor(s): November 20, 2002
  • Published electronically: July 19, 2005
  • Additional Notes: The author thanks Steven Dale Cutkosky for his advice and patience as supervisor for the author’s Ph.D. thesis, and Karen Smith for her advice and help with numerous corrections to this paper.
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 4805-4812
  • MSC (2000): Primary 13A99, 14E99
  • DOI: https://doi.org/10.1090/S0002-9947-05-03866-3
  • MathSciNet review: 2165388