'. Suppose that (R, +,.) be a commutative ring with identity and (I, +,.) be an ideal of R. If I is not prime ideal then (a) 3a, b e R: a. b eI = a ¢ I and b¢ 1 (b) Va, b e R:a. b EI = a ¢ I and b € I (c) Va, b E R: a.b E I= a E I or b eI (d) No Choice

'. Suppose that (R, +,.) be a commutative ring with identity and (I, +,.) be an ideal of R. If I is not prime ideal then (a) 3a, b e R: a. b eI = a ¢ I and b¢ 1 (b) Va, b e R:a. b EI = a ¢ I and b € I (c) Va, b E R: a.b E I= a E I or b eI (d) No Choice

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 36E: 36. Suppose that is a commutative ring with unity and that is an ideal of . Prove that the set of...

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Question

7. Suppose that (R, +,.) be a commutative ring with identity and (I,+,.) be an
ideal of R. If I is not prime ideal then
(a) 3a, b E R:a. b eI = a ¢ I and b ¢ 1
(b) Va, b E R: a. b E I = a ¢ I and b ¢ I
(c) Va, b e R:a. b EI = a E I or b e I
(d) No Choice

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