15 (c) and (d) 15. Let R be the ring of all matrices with integer entries of the form{} ;]=abez}.Show that(a) R is commutative.(b) the mapping : R→ Z given byis a homomorphism.(c) the set{::] ---;]:bez}is an ideal.(d) the set A in (c) above is a prime ideal which is not maximal.{-56

Answered: Image /qna-images/answer/081d39e6-60ce-432b-b253-f5407a55d04e.jpg

Answered: (c) the set b ^ - {[ + ] i>«z} Dez} B…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 22E: 22. Let be a ring with finite number of elements. Show that the characteristic of divides .

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(c) the set b ^ - {[ + ] i>«z} Dez} B is an ideal. (d) the set A in (c) above is a prime ideal which is not maximal.