Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Mixed multiplicities of ideals versus mixed volumes of polytopes
HTML articles powered by AMS MathViewer

by Ngo Viet Trung and Jugal Verma PDF
Trans. Amer. Math. Soc. 359 (2007), 4711-4727 Request permission


The main results of this paper interpret mixed volumes of lattice polytopes as mixed multiplicities of ideals and mixed multiplicities of ideals as Samuel’s multiplicities. In particular, we can give a purely algebraic proof of Bernstein’s theorem which asserts that the number of common zeros of a system of Laurent polynomial equations in the torus is bounded above by the mixed volume of their Newton polytopes.
Similar Articles
Additional Information
  • Ngo Viet Trung
  • Affiliation: Institute of Mathematics, Viên Toán Hoc, 18 Hoàng Quôc Viêt, 10307 Hanoi, Vietnam
  • MR Author ID: 207806
  • Email:
  • Jugal Verma
  • Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India 400076
  • MR Author ID: 177990
  • Email:
  • Received by editor(s): March 1, 2005
  • Received by editor(s) in revised form: March 30, 2005
  • Published electronically: May 1, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 4711-4727
  • MSC (2000): Primary 52B20, 13D40; Secondary 13H15, 05E99
  • DOI:
  • MathSciNet review: 2320648