(A) We have shown that C = { [85]a,bER} is field. Show that CC given by the isomorphism f: C → C where a ² ([$-$$]) = a = a + bi.
(A) We have shown that C = { [85]a,bER} is field. Show that CC given by the isomorphism f: C → C where a ² ([$-$$]) = a = a + bi.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Answer letter A only.
![(A) We have shown that C =
the isomorphism f: C → C where
(B) Suppose char F
=
{ [85]a,bER}
isomorphism f: S → Z).
a
([8 -³])=
a
is field. Show that CC given by
0. Then F contains a subring S such that S≈ Z (i.e. there is an
= a + bi.
g(ab-¹) =
Now, let T = {ab¯¹ | a,b ≤ S, b‡0} and define the map g: T → Q by
f(a)
f(b)
Show that g is an isomorphism so that T ≤ F is isomorphic to Q.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdba100d8-ee81-4676-91a4-e53aa01f96c0%2Fd61a330d-e499-4c18-ba0f-5c767e404188%2Fzu1yzj8_processed.png&w=3840&q=75)
Transcribed Image Text:(A) We have shown that C =
the isomorphism f: C → C where
(B) Suppose char F
=
{ [85]a,bER}
isomorphism f: S → Z).
a
([8 -³])=
a
is field. Show that CC given by
0. Then F contains a subring S such that S≈ Z (i.e. there is an
= a + bi.
g(ab-¹) =
Now, let T = {ab¯¹ | a,b ≤ S, b‡0} and define the map g: T → Q by
f(a)
f(b)
Show that g is an isomorphism so that T ≤ F is isomorphic to Q.
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