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Lüroth field extensions
- Source :
-
Journal of Pure & Applied Algebra . Jul2005, Vol. 199 Issue 1-3, p1-10. 10p. - Publication Year :
- 2005
-
Abstract
- Abstract: Let K be a field of characteristic zero, and let be a purely transcendental field extension of K of transcendence degree . Lüroth''s Theorem. Let E be a subfield of that properly contains the field K. Then for a transcendental element . A field extension is called a Lüroth field extension if and every subfield with is a rational function field in one variable. In this paper, we prove Theorem 1. If F is a Lüroth field extension of field K of characteristic zero that coincides with it''s algebraic closure in F then so is a purely transcendental field extension . As a consequence of this result we have a description of integrally closed subalgebras of of dimension 1. Theorem 2. Suppose, in addition, that K is an algebraically closed field. Let R be a K-subalgebra of the field that is integrally closed in and the transcendence degree of its field of fractions is 1 over K. Then there exists a transcendental element over K such that . [Copyright &y& Elsevier]
- Subjects :
- *ALGEBRA
*ALGEBRAIC field theory
*ABSTRACT algebra
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00224049
- Volume :
- 199
- Issue :
- 1-3
- Database :
- Academic Search Index
- Journal :
- Journal of Pure & Applied Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 17699315
- Full Text :
- https://doi.org/10.1016/j.jpaa.2004.11.003