2. Let R = F[X] and define three different R-module structures on F² (call them V1, V2 and V3), with X acting by 1 1 1 -1 |and a3 1 1 > a2 = repectively. Which of these modules are semisimple and how do they decompose for (а) F — С? (b) F = R ? (c) F = F; ?
2. Let R = F[X] and define three different R-module structures on F² (call them V1, V2 and V3), with X acting by 1 1 1 -1 |and a3 1 1 > a2 = repectively. Which of these modules are semisimple and how do they decompose for (а) F — С? (b) F = R ? (c) F = F; ?
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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hand written plz
![2. Let R = F[X] and define three different R-module structures on F² (call them V1, V2 and V3), with X
acting by
1
1
1
and
=[! ¿]
1
[
a3
repectively. Which of these modules are semisimple and how do they decompose for
||
(b) F = R ?
(c) F = F; ?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a90655e-93a1-4ca7-b657-f9740a9a0a34%2Faf4089d7-244e-4289-a03d-83ff1afa2beb%2Fwke78f_processed.png&w=3840&q=75)
Transcribed Image Text:2. Let R = F[X] and define three different R-module structures on F² (call them V1, V2 and V3), with X
acting by
1
1
1
and
=[! ¿]
1
[
a3
repectively. Which of these modules are semisimple and how do they decompose for
||
(b) F = R ?
(c) F = F; ?
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