From Hermite rings to Sylvester domains

Cohn, P.

doi:10.1090/S0002-9939-99-05189-8

From Hermite rings to Sylvester domains
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by P. M. Cohn

Proc. Amer. Math. Soc. 128 (2000), 1899-1904

DOI: https://doi.org/10.1090/S0002-9939-99-05189-8

Published electronically: November 1, 1999

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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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