Non-commutative Noetherian Rings |
Common terms and phrases
artinian ring Asano right order complete local ring CR¹ defined denote direct sum division ring E C(N elements of Q endomorphism ring epimorphism essential right ideal exists factor ring family of right finitely generated projective follows groupoid H₁ H₂ hence I₁ ideal of Q idempotent implies integral R-ideal isomorphic Jacobson radical K₁ la-P left ideals M-topology max-r and max-l maximal ideal maximal right order min-P minimal prime n+1 n+1 nilpotent ideals non-commutative non-zero ideal P-primary P₁ primary ideal prime ideal prime ring R/P Proof prove R-module regular element right Dedekind right hereditary right Ore condition right quotient ring right R-module ring Q ring with max-r semi-simple simple artin ring simple ring submodule subring suppose symbolic powers theorem 1.1 topological family uniform right ideal unit element unit of Q α α