Hopkins-Levitzki theorem
= Hopkins-Levitzki theorem
{c}
A <right Artinian ring> is a <right Noetherian ring>. Its right regular <module> therefore has finite <composition length>. Its <Jacobson radical> is a <nilpotent ideal>, and its quotient by that <Jacobson radical> is a <semisimple ring>. In particular every finitely generated right <module> over such a <ring> has finite <composition length>.