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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Toward a theory of monomial preorders
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by Gregor Kemper, Ngo Viet Trung and Nguyen Thi Van Anh PDF
Math. Comp. 87 (2018), 2513-2537 Request permission


In this paper we develop a theory of monomial preorders, which differ from the classical notion of monomial orders in that they allow ties between monomials. Since for monomial preorders, the leading ideal is less degenerate than for monomial orders, our results can be used to study problems where monomial orders fail to give a solution. Some of our results are new even in the classical case of monomial orders and in the special case in which the leading ideal defines the tangent cone.
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Additional Information
  • Gregor Kemper
  • Affiliation: Technische Universiät München, Zentrum Mathematik - M11, Boltzmannstr. 3, 85748 Garching, Germany
  • MR Author ID: 608681
  • Email:
  • Ngo Viet Trung
  • Affiliation: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam
  • MR Author ID: 207806
  • Email:
  • Nguyen Thi Van Anh
  • Affiliation: University of Osnabrück, Institut für Mathematik, Albrechtstr. 28 A, 49076 Osnabrück, Germany
  • Email:
  • Received by editor(s): September 16, 2016
  • Received by editor(s) in revised form: April 12, 2017
  • Published electronically: December 28, 2017
  • Additional Notes: The second author was supported by the Vietnam National Foundation for Science and Technology Development under grant number 101.04-2017.19 and the Project VAST.HTQT.NHAT.1/16-18. A large part of the paper was completed during a long term visit of the second author to Vietnam Institute for Advanced Study in Mathematics.
  • © Copyright 2017 American Mathematical Society
  • Journal: Math. Comp. 87 (2018), 2513-2537
  • MSC (2010): Primary 13P10; Secondary 14Qxx, 13H10
  • DOI:
  • MathSciNet review: 3802444