Database of Ring Theory
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Theorems in ring theory
Categories
All theorems
(Uncategorized)
About ideals
Characterization of properties
Connections with dimensions
Connections with modules
Connections with rings of quotients
Properties of constructions
Properties of special subsets
Structure/splitting theorems
Properties of constructions
These describe interplay between properties and constructions
Baker–Heegner–Stark theorem on $\mathbb Q[\sqrt{d}]$
Camillo's theorem on semihereditary polynomial rings
Characterization of self-injective Leavitt path algebras
Formanek-Snider primitive group ring theorem
Inheritance of UFD to power series rings
Kaplansky, Jaffard, Ohm theorem for constructing Bézout domains
Krull's valuation domain theorem
Maschke's Theorem (on when a group algebra is semisimple.)
Semicommutative rings from Armendariz rings
When a group ring is Artinian
When a group ring is hereditary (Dicks's theorem)
When a group ring is linearly compact or algebraically compact
When a group ring is local
When a group ring is Noetherian
When a group ring is perfect
When a group ring is prime
When a group ring is principally injective
When a group ring is self-injective
When a group ring is semilocal
When a group ring is semiprime
When a group ring is von Neumann regular
When a Leavitt path algebra is von Neumann regular
When skew polynomial rings are right duo