Importance of UFDs

$\begingroup$

What is the importance of UFDs?

In course algebra2, we study a lot about UFDs and we check every ring ,which we face in the book or exercises, in order to see that it is UFD or not.

Also, I know this property gives special benefits for a ring But I don't know what are they exactly.

As an example, I know a field has benefits like "it doesn't have proper subfields, two operators creat abelian groups and the second one has one member less than first one and also if we have a maximal subring, we can see that ring over maximal subring is a homomorphism with a field"But I don't know a lot about UFDs.

My question is general and it may be a bit long.

You may write name of a book, magazine, blog, paper, website or a name of a person or a subject in order to find related texts.

I know it can be a bit long so I thank everybody who will answer.

$\endgroup$ 2 Sorted by: Reset to default

Know someone who can answer? Share a link to this question via email, Twitter, or Facebook.

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy