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.