(3) Let I₁ and ₂ are ideals of a ring R. Prove that I₁ U I₂ is an ideal of R if and only if I₁ I₂ or 1₂ C 1₁.

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 4E: Exercises If and are two ideals of the ring , prove that is an ideal of .
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(3)
Let I₁ and ₂ are ideals of a ring R. Prove that
I₁U I₂ is an ideal of R if and only if I₁CI₂ or 12 C 1₁.
Transcribed Image Text:(3) Let I₁ and ₂ are ideals of a ring R. Prove that I₁U I₂ is an ideal of R if and only if I₁CI₂ or 12 C 1₁.
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