Show that the points of intersection of a circle in the plane of a fieldF and a line in the plane of F are points in the plane of F or in theplane of F(√α), where α ∈ F and a is positive. Give an exampleof a circle and a line in the plane of Q whose points of intersectionare not in the plane of Q.

Show that the points of intersection of a circle in the plane of a fieldF and a line in the plane of F are points in the plane of F or in theplane of F(√α), where α ∈ F and a is positive. Give an exampleof a circle and a line in the plane of Q whose points of intersectionare not in the plane of Q.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 3E: Consider the set S={[0],[2],[4],[6],[8],[10],[12],[14],[16]}18, with addition and multiplication as...

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