# 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

Improved ring: Updated ring 50
Sakurai made a single suggestion leading to resolution of 30 properties on $R_{50}$!
new rings/new properties: Hutchins' book
Currently I'm skimming through Hutchins' book (see the bibliography section) trying to make quick additions. Not sure if we'll ever absorb all the examples listed there (180 with pseudo repetition, plus allusions to more).
For those of you with accounts, you'll now see unread message notifications. Also, your profile page looks a lot better.
new ring: $p$-adic numbers
At Sakurai's recommendation, I've added the $p$-adic integers and their number field. Thanks!
new ring: Added Ster's example disproving Morita invariance of "clean"
Added Ster's ring which can be used to show that "clean" is not a Morita invariant property.
new theorem: Thanks Sakurai
Sakurai suggested adding the Akizuki–Hopkins–Levitzki theorem, fill out $F_2[Q_8]$'s properties, and found a few typo corrections. Thanks!
site update: Site improvements
Just rolled out what (I hope) are improvements! You should be able to see some of the changes on the search pages, for example.
new ring: Examples of Bergman and O'Meara
More juicy examples here, here and here. They're all closely related and quite fascinating. The details pages will fill you in!
new ring: Cohn's non IBN domain
I added and example due to Cohn of a domain that doesn't have IBN.
new ring: Added Page's left-not-right FPF ring
Check out Page's example of a one-sided finitely pseudo-Frobenius ring!

## Learn

View a list of resources for studying ring theory.