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Theorems in ring theory
Categories
All theorems
Connections with modules
Properties of constructions
Properties of special subsets
Structure/splitting theorems
(Uncategorized)
Characterization of properties
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Connections with dimensions
About ideals
All theorems available
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OBVIOUS
Conditions equivalent to von Neumann regularity in self-injective rings
Maschke's Theorem (on when a group algebra is semisimple.)
Artin - Wedderburn theorem
Structure of Noetherian distributive rings
When a group ring is self-injective
Akizuki–Hopkins–Levitzki
Amitsur's nil radical theorem
When a group ring is principally injective
Uniserial Noetherian rings
When a group ring is semilocal
When a group ring is local
When a group ring is perfect
$J(R)=\mathcal Z(R_R)$ for principally injective rings
Kaplansky, Jaffard, Ohm theorem for constructing Bézout domains
Krull's valuation domain theorem
fp-injectivity in serial rings
Amitsur-Levitzki theorem
Unit-regular rings are clean
Evans' Cancellation Theorem
Lawrence's theorem on self-injective rings
A right simple-injective, right Kasch ring is right dual
Artinian, Noetherian, semisimple, semiprimitive, primitive are Morita invariant
2-primal implies Dedekind finite
Wedderburn's little theorem
Frobenius' theorem
Jacobson density theorem
Chase's theorem on products of flat modules
Semicommutative rings from Armendariz rings
$soc(_RR)=soc(R_R)$ in dual rings
$\mathcal Z(R_R)\subseteq \ell.ann(soc(R_R))$, and they are equal when $R$ is right Artinian.
Nilpotency of $\mathcal Z(R_R)$
$Nil_\ast(R)\subseteq Nil^\ast(R)\subseteq J(R)$
Structure of self-injective von Neumann regular rings
Commutative equivalents to von Neumann regularity
Baker–Heegner–Stark theorem on $\mathbb Q[\sqrt{d}]$
Characterizations of quasi-Frobenius rings
Characterizations of von Neumann regular rings
Characterizations of hereditary rings
Characterizations of semisimplicity
Characterizations of semiperfect rings
Characterizations of right nonsingular rings
Characterizations of right perfect rings
Goldie's theorem on semisimple classical quotient rings
Ore's theorem on the classical quotient ring of a domain
Classical quotient ring of a commutative reduced ring
Kaplansky's theorem on PI algebras
Camillo's theorem on semihereditary polynomial rings
Krull dimension of an infinite product
Krull dimension of an infinite product of zero dimensional rings
Finite generation of projective ideals
Kaplansky's theorem on modules of right hereditary rings
When a group ring is Artinian
When a group ring is von Neumann regular
When a group ring is Noetherian
When a group ring is hereditary (Dicks's theorem)
When a group ring is prime
Andrunakievič's theorem on subdirect representations of reduced rings