Citations:antirational

Adjective: mathematical sense

 * 1984, Jack Ohm, "On subfields of rational function fields", Archiv der Mathematik, vol. 42, iss. 2, pp. 136-138.
 * From the stronger hypothesis that L is anti-rational over k, Nagata draws the stronger conclusion that L is ~ K.
 * 1976, S. G. Vlèduc, "On the coefficient ring in a semigroup ring", Mathematics of the USSR-Izvestiya, vol. 10, no. 5.
 * If A is an affine algebra whose quotient field Κ is antirational over k, then A is strongly S-invariant.
 * 1987, M. Kang, "The cancellation problem", Journal of Pure and Applied Algebra, vol. 47, pp. 165-171.
 * Let $$\scriptstyle \bar k$$ be the maximal anti-rational subfield of K1(xl, ...,Xn) = K2(Yl,...,Yundefinedn) over k.
 * 1993, Masayoshi Nagata, Theory of Commutative Fields, AMS Bookstore, ISBN 9780821845721, page 125:
 * We say that a field K is antirational over its subfield k if it does not happen that there are a finite algebraic extension K′ of K, an intermediate field K′′ between k and K′, and an element t such that K′ = K′′(t) and t is transcendental over K′′. Namely, K is not antirational over k if there are such K′, K′′, and t.