Let Z[V2] = { a+bv2 ]a,b e Z}. Define addition and multiplication onZ[V2] as follows:(a + bv 2) + (c + dV 2)(a + bv 2) (c+ dv 2)(a + c) + (b + d )V2==(ac+2bd) + (ad + bc)V 2Prove that :Z [V2] is an integral domain

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Let Z[V2] = { a+bv2 la,b e Z}. Define addition and multiplication on Z[V2] (a + bv 2) + (c + d/2) = (a+c)+ (b+ d )/2 (a + bv 2) (c+ dv2) as follows: = (ac+ 2bd) + (ad + bc)/ 2 Prove that : Z [V2] is an integral domain

Let Z[V2] = { a+bv2 la,b e Z}. Define addition and multiplication on Z[V2] (a + bv 2) + (c + d/2) = (a+c)+ (b+ d )/2 (a + bv 2) (c+ dv2) as follows: = (ac+ 2bd) + (ad + bc)/ 2 Prove that : Z [V2] is an integral domain

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let Z[V2] = { a+bv2 ]a,b e Z}. Define addition and multiplication on
Z[V2] as follows:
(a + bv 2) + (c + dV 2)
(a + bv 2) (c+ dv 2)
(a + c) + (b + d )V2
=
=
(ac+2bd) + (ad + bc)V 2
Prove that :
Z [V2] is an integral domain

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