Browse
See rings and properties on record.
All rings »
Commutative rings »
All properties »
Commutative properties »
Search
You can search for rings by their properties. If you are only
interested in commutative rings, try the specialized search with
expanded, commutativeonly properties.
All rings »
Commutative rings »
By keyword »
Contribute
There are a lot of ways you could help, even if you don't
know what specifically what yet.
Make the site better »
Recent activity
Site news RSS »
 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 onesided finitely pseudoFrobenius ring!
 I added Hurwitz and Lipshitz quaternion rings, as well as Gaussian integers.
 I added another classic Bergman example, a rightnotleft 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.
Start learning »
Other helpful sites
If you like this site, then you also might like these sites:
 πBase:
A community database of topological examples with
automated deduction and powerful search
 Math Counterexamples:
Mathematical exceptions to the rules or intuition. (Here you can find
counterexamples from a variety of mathematical disciplines.)
 Graded Ring Database:
A database of graded rings in algebraic geometry
 The Center of Ring Theory and its Applications at Ohio University
 GroupProps the group properties wiki. It has lots of detailed data on specific groups.

The Stacks Project: an open source textbook and reference work on
algebraic stacks and the algebraic geometry needed to define them
 nLab:
a wikilab for collaborative work on Mathematics,
Physics and Philosophy