Show that if E is an algebraic extension of a field F and contains all zeros in F of every f(x) E F[x], then E is an algebraically closed field.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.2: Ring Homomorphisms
Problem 28E
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Section 31 Number 34
Section 32
Geometric Constructions
293
34. Show that if E is an algebraic extension of a field F and contains all zeros in F of every f(x) E F [x], then E
is an algebraically closed field.
Transcribed Image Text:Section 32 Geometric Constructions 293 34. Show that if E is an algebraic extension of a field F and contains all zeros in F of every f(x) E F [x], then E is an algebraically closed field.
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