F onto a subfield of an algebraic closure F Theory 9. Let Z2 be an algebraic closure of Z2, and let a, ß e Z, be zeros of x³ +x² + 1 and of x³ +x+1,respectively. Using the results of this section, show that Z2(a) = Z2(B). 0. Show that every irreducible polvnomial in

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Section 33 number 9
Ing F onto a subfield of an algebraic closure F
Theory
9. Let Z2 be an algebraic closure of Z2, and let a, ß e Z, be zeros of x³ +x² + 1 and of x +x+1, respectively.
Using the results of this section, show that ZL@) = Z2(B).
10. Show that every irreducible nolynomial in
Transcribed Image Text:Ing F onto a subfield of an algebraic closure F Theory 9. Let Z2 be an algebraic closure of Z2, and let a, ß e Z, be zeros of x³ +x² + 1 and of x +x+1, respectively. Using the results of this section, show that ZL@) = Z2(B). 10. Show that every irreducible nolynomial in
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