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

See rings and properties on record.

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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.

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).

site news: On-site notifications

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

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!

View a list of resources for studying ring theory.

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