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Polynomial Rings and Composition Series

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Let R = Q[X,Y] be the polynomial ring in two variables. Show that the R-module R/(X^2 -Y) has no composition series.

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Polynomial rings and composition series are investigated.

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Proof:
Suppose the -module has a composition series as follows.

Then we have

The composition factors are , .
Since each composition factor is simple, then is the proper ...

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