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Prove that (x, y) and (2, x, y) are prime ideals in Z[x, y] but only the latter ideal is a maximal ideal.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.2: Divisibility And Greatest Common Divisor

Problem 34E

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Prove that (x, y) and (2, x, y) are prime ideals in Z[x, y] but only the latter ideal is a
maximal ideal.

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