Answered: Let f∶ R → S be a ring…

Let f∶ R → S be a ring homomorphism,with R and S commutative.If P is a prime ideal of S,show that the preimage f^(-1) (P) is a prime ideal of R

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 → S be a ring homomorphism,with R and S commutative.If P is a prime ideal of S,show that the preimage f^(-1) (P) is a prime ideal of R

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