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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Henselian fields and solid $ k$-varieties. II


Author: Gustave Efroymson
Journal: Proc. Amer. Math. Soc. 35 (1972), 362-366
MSC: Primary 14G20; Secondary 13J15
MathSciNet review: 0318160
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Abstract: Let k be a real closed or Henselian field. A k-variety X (affine) is said to be solid if X is determined by its k points. It is shown that a k-variety is solid if and only if it contains a nonsingular k point. Another condition for solidity is given and a dimension theorem indicated.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0318160-2
PII: S 0002-9939(1972)0318160-2
Keywords: Solid k-variety, Henselian field, real closed field, implicit function theorem
Article copyright: © Copyright 1972 American Mathematical Society