# Topics in Abstract Algebra/Non-commutative rings

(Redirected from Introduction to Rings and Algebras/Non-commutative rings)
Proposition. Let $R$ be a simple ring. Then
• (i) Every morphism $R\to R$ is either zero or an isomorphism. (Schur's lemma)
Theorem (Levitzky). Let $R$ be a right noetherian ring. Then every (left or right) nil ideal is nilpotent.