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.

All rings » Commutative rings »

View a list of resources for studying ring theory.

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

new ring: Right-not-left free ideal ring

JeremyRickard suggested an example of a right free ideal ring that does not satisfy the ACC on left principal ideals.

new ring: the Toeplitz-Jacobson algebra

Thanks dbossaller for the excellent example of a ring which has IBN but is not Dedekind finite.

New ring: Cozzens' simple left PID

This example due to Cozzens is often cited as showing how much asymmetry is possible in simple rings.

new theorem: Did you know...

Commutative von Neumann regular rings are characterized by the fact that their polynomial ring over a single variable is semihereditary? That is the content of this theorem of Camillo.

new ring: Almost-but-not-quite-Dedekind

Added an example of an almost Dedekind ring which isn't Dedekind. In particular it has Krull dimension 1, all of its localizations are Noetherian, but it itself is not Noetherian.

New ring: asymmetry of PF

new ring: Asymmetry of principally injective

This is an example of a ring which is one-sided principally injective.

New rings: V domains

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.

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