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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The ruled residue theorem for simple transcendental extensions of valued fields


Author: Jack Ohm
Journal: Proc. Amer. Math. Soc. 89 (1983), 16-18
MSC: Primary 12F20; Secondary 13A18
MathSciNet review: 706500
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Abstract: A proof is given for the Ruled Residue Conjecture, which asserts that if $ \upsilon $ is a valuation of a simple transcendental field extension $ {K_0}(x)$ and $ {\upsilon _0}$ is the restriction of $ \upsilon $ to $ {K_0}$, then the residue field of $ \upsilon $ is either ruled or algebraic over the residue field of $ {\upsilon _0}$.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0706500-9
Keywords: Valued fields, simple transcendental field extensions, ruled field extensions
Article copyright: © Copyright 1983 American Mathematical Society