E M 4.ll Asiacelldocs.google.com/forms7. Suppose that (R, +,.) be a commutative ring with identity and (I, +,.) be anideal of R. If I is not prime ideal then.....(a) 3a, b e R:a.beI = a ¢ I and b € 1(b) Va, bE R: a. bel = a ¢ I and b ¢I(c) Va, beR: a. beI = a El or bel(d) No Choice(a)(b)(c)(d)8. In the field (Z,, +7,.7), the set of all prime elements is...(а) ф(b) {2,3,5}(c) Z,(d) No Choice(a)(b)(c)(d)...

Prime Ideal:- An ideal P of a commutative ring R is prime if it has the following two properties:…

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.beI = a € and b € I (b) Va, be R: a. beI > a ¢ I and b e I (c) va, be R:a.beI = a € l or bel (d) No Choice (a) (b) (c) (d) O 8. In the field (Z,, +7,.7), the set of all prime elements is... (a) p (b) (2,3,5} (c) Z, (d) No Choice (a) (b) (c) (d)

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.beI = a € and b € I (b) Va, be R: a. beI > a ¢ I and b e I (c) va, be R:a.beI = a € l or bel (d) No Choice (a) (b) (c) (d) O 8. In the field (Z,, +7,.7), the set of all prime elements is... (a) p (b) (2,3,5} (c) Z, (d) No Choice (a) (b) (c) (d)

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 31E: Let R be a commutative ring that does not have a unity. For a fixed aR, prove that the set...

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