4. In Z[r], let I = {f(x) E Z[r] | f (0) is even}.(a) Prove that I = (x, 2).(b) Show that I is maximal in Z[x].(c) Describe the elements in Z[x]/I.

Name: 4. In Z[r], let I = {f(x) E Z[r] | f (0) is even}.(a) Prove that I =
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Description: 4. In Z[r], let I = {f(x) E Z[r] | f (0) is even}.(a) Prove that I = (x, 2).(b) Show that I is maximal in Z[x].(c) Describe the elements in Z[x]/I.

Given, In Zx, let I=fx∈Zx | f(0) is even (a) Prove that I=x, 2 Let…

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In Z[r], let I = {f(x) E Z[r] | f(0) is even}. (a) Prove that I = (x, 2). (b) Show that I is maximal in Z[r]. (c) Describe the elements in Z[r]/I.

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 26E: Prove that every ordered integral domain has characteristic zero.

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