# Welcome to the Database of Ring Theory!

A repository of rings, their properties, and more ring theory stuff.

## Browse

See rings and properties on record.

## Search

You can search for rings by their properties. If you are only interested in commutative rings, try the specialized search with expanded, commutative-only properties.

## Contribute

There are a lot of ways you could help, even if you don't know what specifically what yet.

### Recent activity

• At Sakurai's recommendation, I've added the $p$-adic integers and their number field. Thanks!
• Added Ster's ring which can be used to show that "clean" is not a Morita invariant property.
• Sakurai suggested adding the Akizuki–Hopkins–Levitzki theorem, fill out $F_2[Q_8]$'s properties, and found a few typo corrections. Thanks!
• Just rolled out what (I hope) are improvements! You should be able to see some of the changes on the search pages, for example.
• More juicy examples here, here and here. They're all closely related and quite fascinating. The details pages will fill you in!
• I added and example due to Cohn of a domain that doesn't have IBN.
• Check out Page's example of a one-sided finitely pseudo-Frobenius ring!
• I added Hurwitz and Lipshitz quaternion rings, as well as Gaussian integers.
• I added another classic Bergman example, a right-not-left primitive ring. For a long time I thought it was already entered... Bergman has so many amazing examples!
• I added Nakayama's example of a QF ring that isn't Frobenius! Can't believe I didn't add it a long time ago...

## Learn

View a list of resources for studying ring theory.