Purchase Solution

Maximal Ideals, Residues and Ring Homomorphisms

Not what you're looking for?

Ask Custom Question

Let . Show that the map the residue of a+ b modulo 2, is a ring homomorphism with . Prove that . Hence, or otherwise, give a maximal ideal of .
Consider the ideal (2)+(x) of . Show that (2)+(x) . Hence explain why (x) is not a maximal ideal of .

NOTE: All question marks are Z, the integers

Please see the attached file for the fully formatted problems.

Attachments
Purchase this Solution

Solution Summary

Maximal Ideals, Residues and Ring Homomorphisms are investigated. The solution is detailed and well presented.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

1. Proof:
For any , we have

Here we use the fact that in ...

Purchase this Solution


Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

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

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

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.