i need the answer quickly (1) Let I be a proper ideal of the commutative ring R with identity. Then Iis a ........ if and only if the quotient ring R/I is a field.(i) prime ideal (ii) primary ideal (iii) Maximal ideal

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Answered: (1) Let I be a proper ideal of the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.1: Polynomials Over A Ring

Problem 15E: 15. Prove that if is an ideal in a commutative ring with unity, then is an ideal in .

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(1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and only if the quotient ring R/I is a field. (i) prime ideal (ii) primary ideal (iii) Maximal ideal