Let R be a commutative ring with 1 and I be a proper ideal of R. Prove that I is prime if and only if R/I is an integral domain.
Let R be a commutative ring with 1 and I be a proper ideal of R. Prove that I is prime if and only if R/I is an integral domain.
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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