Problem two : Consider the rings Z[V10] and the ring of integers Z. Define the map $: Z[V10] →Z with: (A) = A.A where A is the conjugate of A. Answer the following: (a) Does o define a ring homomorphism? (b) Show that A is a unit in Z[V10] if and only if (A) = ±1. %3D

Problem two : Consider the rings Z[V10] and the ring of integers Z. Define the map $: Z[V10] →Z with: (A) = A.A where A is the conjugate of A. Answer the following: (a) Does o define a ring homomorphism? (b) Show that A is a unit in Z[V10] if and only if (A) = ±1. %3D

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 10E: Let R be a commutative ring with characteristic 2. Show that each of the following is true for all...

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Problem two :
Consider the rings Z[V10] and the ring of integers Z. Define the map
0: Z[V10] Z
with: (A) = A.A where A is the conjugate of A. Answer the following:
(a) Does o define a ring homomorphism?
(b) Show that A is a unit in Z[V10] if and only if ø(A) = ±l.
%3D

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