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The transcendence degree of an integral domain over a subfield and the dimension of the domain

Published online by Cambridge University Press:  22 January 2016

Hiroshi Tanimoto
Hiroshi Tanimoto*
Affiliation:
Department of Mathematics, Faculty of Education and Culture, Miyazaki University, Miyazaki 889-2192, Japan, [email protected]
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Abstract

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For a domain A containing a field k with tr.degkA < ∞, we define a new transcendence degree of A with respect to k, which is denoted by tdkA. By using this, we generalize the theorem that for every affine domain A over a field k it holds that dim A = tr.degkA. For example, we show that if A is a quasi-local domain containing a field k with dim A = tdkA < ∞, then for every Noetherian local k-subalgebra R of A it holds that dim R = tdkR. Moreover we also generalize the theorem due to Gilmer, Nashier and Nichols.

Keywords

13C1513E0513B30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 170 , 2003 , pp. 145 - 162
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

References

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