Subsets of fields whose nth-root functions are rational functions
-
David E. Dobbs [1]
-
[1] University of Tennessee
-
- Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 49, Nº. 6, 2018, págs. 948-958
- Idioma: inglés
- DOI: 10.1080/0020739x.2017.1423122
- Texto completo no disponible (Saber más ...)
-
Resumen
Let R be an integral domain with quotient field F, let S be a non-empty subset of R and let n 2 be an integer. If there exists a rational function ϕ: S → F such that ϕ(a) n = a for all a S, then S is finite. As a consequence, if F is an ordered field (for instance, R) and S is an open interval in F, no such rational function ϕ exists. Applications to finite fields and additional examples are given. The methods used are algebraic. A closing remark indicates how this note could be used as enrichment material in courses ranging from precalculus to undergraduate courses on abstract algebra or analysis.
¿Es nuevo? Regístrese
Ventajas de registrarse
