Abstract
The theory of Noetherian rings may be said to have begun with Goldie's 1958 paper. Since then the theory has steadily gathered strength. By now, various methods and results from the theory of commutative Noetherian rings have been adapted to non-commutative Noetherian rings. The theory has also contributed to and benefitted from developments in three nearby areas: P.I. rings, enveloping algebras of Lie algebras, and group rings of polycyclic-by-finite groups.
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