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.

- I added several interesting examples for clean/nonclean rings which I found while reading Nicholas A. Immormino's dissertation "Clean rings & clean group rings." (2013)
- jose.simental helped add $13$ new properties to Local Cohen-Macaulay domain which isn't regular
- jose.simental suggested adding the ring of differential operators on a line, as well as Maschke's theorem.
- Soumitra.3 helped add 7 more properties for Osofsky's 32 element ring.
- Wanted: a ring whose nilpotent elements form an ideal strictly smaller than the intersection of prime ideals.
- Added $k[[x^2,x^3]]$ after finding it on math.SE
- Admins can now give feedback on your suggestions via your profile page. Such feedback will appear (if it exists) right below the suggestion.
- Watson contributed commutative, perfect, non-Artinian ring!
- Watson contributed a local ring with an infinite prime spectrum!

View a list of resources for studying ring theory.

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- The Center of Ring Theory and its Applications at Ohio University
- 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