# Ring Homomorphisms, Residues and Distinct Maximal Ideals

Not what you're looking for? Search our solutions OR ask your own Custom question.

Let . Prove that the map given by , where is the residue of a modulo n, is a ring homomorphism. Find the kernel and image of .

Prove that if is a ring homomorphism, then given by is also a ring homomorphism.

Write down two distinct maximal ideals of . Does have a finite or infinite number of maximal ideals? Give brief reasons for your answer.

Please see the attached file for the fully formatted problems.

Â© BrainMass Inc. brainmass.com September 28, 2022, 9:04 pm ad1c9bdddfhttps://brainmass.com/math/ring-theory/ring-homomorphisms-residues-distinct-maximal-ideals-54471

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

1. Proof:

Since is a ring, then for any , we have (mod ) (mod ) (mod ). (mod ) (mod ) (mod ). Thus for any , ...

#### Solution Summary

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

$2.49