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A note on trascendental elements of an algebraic function field of one variable
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:  29Feb1972 
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.1317; 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 adbc≠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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