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
Connections with modules
Theorems linking ring theoretic properties to categories of modules
Akizuki–Hopkins–Levitzki
Artinian, Noetherian, semisimple, semiprimitive, primitive are Morita invariant
Characterizations of hereditary rings
Characterizations of quasi-Frobenius rings
Characterizations of right nonsingular rings
Characterizations of right perfect rings
Characterizations of self-injective rings
Characterizations of semiperfect rings
Characterizations of semisimplicity
Characterizations of von Neumann regular rings
Chase's theorem on products of flat modules
Evans' Cancellation Theorem
Kaplansky's theorem on modules of right hereditary rings
Kaplansky's theorem on projective modules over a local ring