Citations:antirational

Adjective: mathematical sense

• 1984, Jack Ohm, "On subfields of rational function fields", Archiv der Mathematik, vol. 42, iss. 2, pp. 136-138 [1].

  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. [2]

  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. [3]

  Let $\overline{k}$ be the maximal anti-rational subfield of K₁(x_l, ...,X_n) = K₂(Y_l,...,Yn) over k.

• 1993, Masayoshi Nagata, Theory of Commutative Fields, AMS Bookstore, Template:ISBN, 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 Template:Nowrap of K, an intermediate field Template:Nowrap between k and Template:Nowrap, and an element t such that Template:Nowrap = Template:Nowrap and t is transcendental over Template:Nowrap. Namely, K is not antirational over k if there are such Template:Nowrap, Template:Nowrap, and t.