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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

From Hermite rings to Sylvester domains


Author: P. M. Cohn
Journal: Proc. Amer. Math. Soc. 128 (2000), 1899-1904
MSC (1991): Primary 16E60; Secondary 15A30, 16D40
Published electronically: November 1, 1999
MathSciNet review: 1646314
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05189-8
PII: S 0002-9939(99)05189-8
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
Article copyright: © Copyright 2000 American Mathematical Society