Let F be a field and let f(x) be a polynomial in F[x] that is reducible over F. Then * < f(x) > is a prime ideal but not maximal in F[x] is maximal in F[x] None of the choices is not a prime ideal in F[x]

Let F be a field and let f(x) be a polynomial in F[x] that is reducible over F. Then * < f(x) > is a prime ideal but not maximal in F[x] is maximal in F[x] None of the choices is not a prime ideal in F[x]

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 4TFE: True or False Label each of the following statements as either true or false. 4. Any polynomial of...

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Question

False
True
Let F be a field and let f(x) be a polynomial in F[x] that is reducible over F.
Then *
<f(x) > is a prime ideal but not maximal in F[x]
<f(x) > is maximal in F[x]
None of the choices
<f(x) > is not a prime ideal in F[x]
Which cf the followingassertions is true
e here to search
88 F
TOSHIBA

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