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A note on trascendental elements of an algebraic function field of one variable

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Title: A note on trascendental elements of an algebraic function field of one variable
Authors: Washio, Tadashi
Authors (alternative): 鷲尾, 忠司
Issue Date: 29-Feb-1972
Publisher: 長崎大学教育学部
Citation: 長崎大学教育学部自然科学研究報告. vol.23, p.13-17; 1972
Abstract: Let K be an algebraic function field of one variable with a constant field k. We shall assume that K is separably generated over k and then we shall denote by x a separating element of K over k. The purpose of this note is to discuss the problem whether we can find the elements a, b, c, d, in k satisfying ad-bc≠O such that every prime divisor of K that divides the denominator divisor or the numerator divisor of the elemerit of the from ax+b/cx+d is unramified over the rational function field k(x), or not. It is obvious that we can find such elements if k is not finite. But it is impossible in general if k is finite. In §2, we shall prove that there exist such elements in k under some condition, and we shall show that this is the best condition in a sense in §3.
URI: http://hdl.handle.net/10069/33017
ISSN: 0386443X
Type: Departmental Bulletin Paper
Text Version: publisher
Appears in Collections:No. 23

Citable URI : http://hdl.handle.net/10069/33017

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