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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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From Hermite rings to Sylvester domains
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by P. M. Cohn PDF
Proc. Amer. Math. Soc. 128 (2000), 1899-1904 Request permission

Abstract:

The main result proved here is a new criterion for a ring to be a Sylvester domain, and so to have a universal skew field of fractions inverting all full matrices: An Hermite ring is a Sylvester domain if and only if any product of full matrices (when defined) is full. This is also shown to hold if (and only if) the set of all full matrices is lower multiplicative. The definition of Hermite rings is weakened, but it is shown that in any case infinitely many sentences are needed.
References
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  • P. M. Cohn, Universal Algebra (revised and enlarged edition), D. Reidel, Dordrecht-Boston, 1981.
  • P. M. Cohn, Free rings and their relations, 2nd ed., London Mathematical Society Monographs, vol. 19, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1985. MR 800091
  • P. M. Cohn, Skew fields, Encyclopedia of Mathematics and its Applications, vol. 57, Cambridge University Press, Cambridge, 1995. Theory of general division rings. MR 1349108, DOI 10.1017/CBO9781139087193
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Additional Information
  • P. M. Cohn
  • Affiliation: University College London, Gower Street, London WC1E 6BT, United Kingdom
  • Email: pmc@math.ucl.ac.uk
  • Received by editor(s): April 17, 1998
  • Received by editor(s) in revised form: August 24, 1998
  • Published electronically: November 1, 1999
  • Communicated by: Ken Goodearl
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 1899-1904
  • MSC (1991): Primary 16E60; Secondary 15A30, 16D40
  • DOI: https://doi.org/10.1090/S0002-9939-99-05189-8
  • MathSciNet review: 1646314