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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
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.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 2003
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