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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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.
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