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
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Chapter2: Second-order Linear Odes
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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; ?
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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