复数域上二元超越扩张的若干性质

ON PROPERTY OF EXTENSION FIELD WITH TWO VARIABLES OVER COMPLBX NUMBER FIELD C

讨论复数域上超越扩域的代数扩张是研究一般域扩张的重要途径，本文考虑了如下的问题：设ｕ是Ｃ上超越元，代数扩张以Ｃ（ｕ，ｔ）／Ｃ（ｕ￣ｎ，ｔ￣ｎ）具有何种性质。证明了对于某些三元组（ｋ，ｅ，ｎ）＝Ｃ（ｕ￣ｎ，ｔ￣ｎ）。

It is important to research the field extension by the way of discussing the algebraicextension over the transcendental extension field over C,In this paper we consider the followingproblem : Let u be a transcendemtal element over C,then what can wesay about the algebraic extension of C(u,t)/C(u￣n,t￣n). We prove that for some triples(k,e,n),C(u,t)=C(u￣n,t￣n).