Welcome to the Database of Ring Theory!

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

Learn more »

Browse

See rings and properties on record.

All rings » Commutative rings »

All properties » Commutative properties »

By dimension »

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.

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 »

New ring: asymmetry of PF
This is a ring which is one-sided pseudo-Frobenius. The construction is involved, and not complete yet. Also, if you had any trouble visiting the theorems section recently, please try again. I fixed a bug there.
new ring: Asymmetry of principally injective
This is an example of a ring which is one-sided principally injective.
New rings: V domains
Added this ring and this ring, examples of simple right V domains, which I hear are pretty rare.
Site news: Ring maps
I posted a few graphs of implications between ring properties. This is the first time I've regenerated the graphs in a long time, so there are probably problems. Please let me know if you find any. Thanks!
site news: 100th ring winner (and more!)
Congratulations MatheinBoulomenos for the winning submission! The next several rings are submissions from the contest too, so check them out. Also thanks to kc_kennylau for working so hard filling in a lot of gaps, especially around ring cardinalities.
site news: 100th ring competition
Would you like to be the contributor for the 100th ring on the Database of Ring Theory? Register and submit your suggestion at https://ringtheory.herokuapp.com/contribute/ , and your username will adorn the entry. (See, e.g. https://ringtheory.herokuapp.com/rings/ring/99/ ) See the details at https://plus.google.com/u/0/+RyanSchwiebert112358/posts/Hor8wApw3YL
site news: "Corrections to Examples of Commutative rings"
Put up the first draft of a TeX document of errata for Examples of Commutative rings. Find the link on the errata page.
site update: Dimensions page
Owing to the difficulties of sensibly ordering and searching dimensions, I've settled on this presentation of dimensions. As always, if some data is missing, please submit it for entry!
Site update: Three new features!
On ring detail pages you will now find Dimensions and Subsets tabs. Take a look at $\mathbb Z$ to see how they work. Also, there is now a ring theory literature errata page so we can track mistakes as we find them. You can get to it through the Citations menu item.
new property: PCI rings
I added PCI rings to the collection. Interestingly, this is the only property I'm aware of in the database for which it is currently unknown whether or not the definition is symmetric or asymmetric.

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: