Editing Ring theory (section)

==Some relevant theorems==
General
*[[Isomorphism theorem#Rings|Isomorphism theorems for rings]]
*[[Nakayama's lemma]]

Structure theorems
*The [[Artin–Wedderburn theorem]] determines the structure of [[semisimple ring]]s
*The [[Jacobson density theorem]] determines the structure of [[primitive ring]]s
*[[Goldie's theorem]] determines the structure of [[semiprime ideal|semiprime]] [[Goldie ring]]s
*The [[Zariski–Samuel theorem]] determines the structure of a commutative [[principal ideal ring]]
*The [[Hopkins–Levitzki theorem]] gives necessary and sufficient conditions for a [[Noetherian ring]] to be an [[Artinian ring]]
*[[Morita theory]] consists of theorems determining when two rings have "equivalent" module categories
*[[Cartan–Brauer–Hua theorem]] gives insight on the structure of [[division ring]]s
*[[Wedderburn's little theorem]] states that finite [[domain (ring theory)|domains]] are [[field (mathematics)|fields]]

Other
*The [[Skolem–Noether theorem]] characterizes the [[automorphism]]s of [[simple ring]]s