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Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.4: Maximal Ideals (optional)

Problem 28E: If R is a finite commutative ring with unity, prove that every prime ideal of R is a maximal ideal...

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Let f: R→ R' be a ring homomorphism of commutative rings R and R'. Show that if the ideal P is
a prime ideal of R' and f-¹(P) ‡ R, then the ideal f-¹(P) is a prime ideal of R.
[Note: f-¹(P) = {a € R| f(a) = P}]

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