# Polynomial Rings and Composition Series

Not what you're looking for?

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.

##### Purchase this Solution

##### Solution Summary

Polynomial rings and composition series are investigated.

##### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

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 ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Probability Quiz

Some questions on probability

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.