Let K be an extension of a field F. If a, be K arealgebraic over F, then a ±b, ab, ab' (b# 0) are algebraic over F. In otherwords, the elements of K which are algebraic over F form a subfield of K.

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Answered: Let K be an extension of a field F. If…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 18E

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Let K be an extension of a field F. If a, be K are algebraic over F, then a± b, ab, ab (b#0) are algebraic over F. In other words, the elements of K which are algebraic over F form a subfield of K.