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

See rings and properties on record.

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All properties » Commutative properties »

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.

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

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.

rings improved: Thanks KMattis!

As a result of two or three suggestions left by KMattis, a total of around 100 properties on a handful of rings were decided. Thanks! A good example of how sometimes just a few suggestions can snowball into an avalanche.

new ring: Right-not-left V ring

From Michler and Villemayor's classic paper, I've added the example they gave to prove asymmetry of V rings.

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).

View a list of resources for studying ring theory.

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