Subsets of Fields Whose nth-Root Functions Are Rational Functions

Autor/in	Dobbs, David E.
Titel	Subsets of Fields Whose nth-Root Functions Are Rational Functions
Quelle	In: International Journal of Mathematical Education in Science and Technology, 49 (2018) 6, S.948-958 (11 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Dobbs, David E.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2017.1423122
Schlagwörter	Numbers; Mathematics Instruction; Algebra; Mathematical Formulas; Mathematical Applications; Mathematical Logic; Validity + Suchen Sie Ihr Suchwort? Zahlenraum; Mathematics lessons; Mathematikunterricht; Mathematische Formel; Angewandte Mathematik; Innermathematische Anwendung; Mathematical logics; Mathematische Logik; Gültigkeit
Abstract	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 ?: S [right arrow] F such that ?(a)[superscript n] = a for all a ? S, then S is finite. As a consequence, if F is an ordered field (for instance,[real numbers]) and S is an open interval in F, no such rational function ? 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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01