Non-Noetherian Ring - Pure Mathematics - Algebra Dictionary Definition A ring (usually commutative with unity in this context) that does not satisfy the ascending chain condition on ideals: there exists an infinite strictly ascending chain of ideals, and ideals need not be finitely generated.
Non-Noetherian Ring - Pure Mathematics - Algebra Dictionary Definition A ring (usually commutative with unity in this context) that does not satisfy the ascending chain condition on ideals: there exists an infinite strictly ascending chain of ideals, and ideals need not be finitely generated.