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Going-down underrings

Published online by Cambridge University Press:  17 April 2009

David E. Dobbs
David E. Dobbs
Affiliation:
Department of Mathematics, University of Tennessee Knoxville, Tennessee 37996, U.S.A.
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Let R be an integral domain with quotient field K. Ten conditions equivalent to “Either R is algebraic over ℤ or t.d.(R/Fp) ≤ 1 for some p” are given. One of these conditions, referred to in the title, is “Each extension of subrings of R having quotient field K satisfies the going-down property.” As consequences, other classes of rings are also characterised.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 3 , December 1987 , pp. 503 - 513
Copyright
Copyright © Australian Mathematical Society 1987

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