Topics in Abstract Algebra/Non-commutative rings
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A ring is not necessarily commutative but is assumed to have the multiplicative identity.
Proposition. Let be a simple ring. Then
- (i) Every morphism is either zero or an isomorphism. (Schur's lemma)
Theorem (Levitzky). Let be a right noetherian ring. Then every (left or right) nil ideal is nilpotent.