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ERIC Number: EJ1183337
Record Type: Journal
Publication Date: 2018
Pages: 11
Abstractor: As Provided
ISSN: ISSN-0020-739X
Subsets of Fields Whose nth-Root Functions Are Rational Functions
Dobbs, David E.
International Journal of Mathematical Education in Science and Technology, v49 n6 p948-958 2018
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.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A