**ERIC Number:**EJ1183337

**Record Type:**Journal

**Publication Date:**2018

**Pages:**11

**Abstractor:**As Provided

**ISBN:**N/A

**ISSN:**ISSN-0020-739X

Subsets of Fields Whose nth-Root Functions Are Rational Functions

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.

Descriptors: Numbers, Mathematics Instruction, Algebra, Mathematical Formulas, Mathematical Applications, Mathematical Logic, Validity

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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