Definition:Noetherian Ring
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Definition
Definition 1
A commutative ring with unity $A$ is Noetherian if and only if every ideal of $A$ is finitely generated.
Definition 2
A commutative ring with unity $A$ is Noetherian if and only if it satisfies the ascending chain condition on ideals.
Definition 3
A commutative ring with unity $A$ is Noetherian if and only if it satisfies the maximal condition on ideals.
Definition 4
A commutative ring with unity $A$ is Noetherian if and only if it is Noetherian as an $A$-module.
Also known as
Some sources render the term Noetherian ring as noetherian, dropping the capital N.
Also see
- Results about Noetherian rings can be found here.
Source of Name
This entry was named for Emmy Noether.