The ruled residue theorem for simple transcendental extensions of valued fields
HTML articles powered by AMS MathViewer
- by Jack Ohm PDF
- Proc. Amer. Math. Soc. 89 (1983), 16-18 Request permission
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 ${\upsilon _0}$.References
- William J. Heinzer, Valuation rings and simple transcendental field extensions, J. Pure Appl. Algebra 26 (1982), no. 2, 189–190. MR 675015, DOI 10.1016/0022-4049(82)90024-X
- Masayoshi Nagata, A theorem on valuation rings and its applications, Nagoya Math. J. 29 (1967), 85–91. MR 207688
- Jack Ohm, Simple transcendental extensions of valued fields, J. Math. Kyoto Univ. 22 (1982/83), no. 2, 201–221. MR 666971, DOI 10.1215/kjm/1250521810
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 16-18
- MSC: Primary 12F20; Secondary 13A18
- DOI: https://doi.org/10.1090/S0002-9939-1983-0706500-9
- MathSciNet review: 706500