Please do no 12 (ii) 2, is a field.(iii) pZ is a prime ideal.(12) Given the set of 2 x 2 matrices with integer entries of the formbaShow that I(i) R is a commutative ring.(ii) the mapping : R-Z given byis a homomorphism(iii) the setR=Show that(i) R is a commutative ring.(ii) the setis a homomorphism.Scientific WorkPlaceis a prime ideal which is not maximal.(13) Let R be the set of all matrices with rational entries, M₁(Q), of the formis an ideal of R.(iii) A is a maximal ideal of R.(iv) the mapping : R Q given byhb -b-b boabe0 a b00 aa+bb c--{:::~}000.be 2a be0 g b00 a= a

Answered: Image /qna-images/answer/f9189e6f-9af5-40a8-907c-af42d105ef55.jpg

Answered: (ii) 2, is a field. (iii) pZ is a prime…

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 26E: . a. Let, and . Show that and are only ideals of and hence is a maximal ideal. b. Show...

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