| An initial algebra is an algebra which is obtained from a subalgebra of some ambient algebra analogous to the initial ideal of an ideal in Groebner basis theory. To find hidden properties of subalgebras, it is sometimes useful to study their initial algebras. In general, however, it is not easy to determine the structure of the initial algebra of a given subalgebra. In this talk, we determine the structure of the initial algebra of a certain subalgebra of a field. As an application of our main theorem, we arrange the proof of the Jung-van der Kulk theorem on polynomial automorphisms given by Makar-Limanov which was modified by Dicks and by Cohn. |