Exercise 13.5. Let R be a commutative ring and P be a proper ideal of R. Show that P is a prime ideal of R if and only if for every two ideal I and J of R, one has IJCP ICP or JC P.

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 3E
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Exercise 13.5. Let R be a commutative ring and P be a proper ideal of R. Show that P is a
prime ideal of R if and only if for every two ideal I and J of R, one has
IJCP ICP or JC P.
Transcribed Image Text:Exercise 13.5. Let R be a commutative ring and P be a proper ideal of R. Show that P is a prime ideal of R if and only if for every two ideal I and J of R, one has IJCP ICP or JC P.
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