Let P be a prime ideal and R a commutative ring with identity. If R/P is an integral domain, explain why R/P cannot be the ring with one element. Also explain why P is not equal to R in this scenario.

Let P be a prime ideal and R a commutative ring with identity. If R/P is an integral domain, explain why R/P cannot be the ring with one element. Also explain why P is not equal to R in this scenario.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 35E: Let R be a commutative ring with unity whose only ideals are {0} and R Prove that R is a...

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