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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.

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    $\begingroup$ See the following questions: here, here, here, and several other references. $\endgroup$ May 1, 2017 at 11:11
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    $\begingroup$ Reading the equivalent characterizations will help a lot, I hope. But in general, the usefulness of unique factorizations seems pretty self-explanatory. Imagine trying to explain chemistry without the concepts of atoms or how they combine "uniquely" to produce different molecules. (scare quotes around "uniquely" are meant to take care of the finer points of what that would mean. Suffice it to say that fixed types of molecules have certain invariants.) $\endgroup$
    – rschwieb
    May 1, 2017 at 13:12

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