T = a 0 d]||a, c, d = Q} and = { [ ]|₁ € Q} U = of the matrix ring M₂(Q). Show that U is an ideal in the subring T but not an ideal in M₂(Q).
T = a 0 d]||a, c, d = Q} and = { [ ]|₁ € Q} U = of the matrix ring M₂(Q). Show that U is an ideal in the subring T but not an ideal in M₂(Q).
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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RINGS/ GROUPS THEORY
====
Consider the subrings T and U as in the picture
![a
T-{[83]|4,5400}
a,
d
=
and
*- {[ ]|c=a}
U =
of the matrix ring M₂(Q).
Show that U is an ideal in the subring T but not an ideal in M₂(Q).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09c2f836-a777-444b-9271-94b360db7692%2Fdd02e561-cc82-4d64-945d-dc9614c62aa4%2Foqva02_processed.png&w=3840&q=75)
Transcribed Image Text:a
T-{[83]|4,5400}
a,
d
=
and
*- {[ ]|c=a}
U =
of the matrix ring M₂(Q).
Show that U is an ideal in the subring T but not an ideal in M₂(Q).
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