Noetherian: Let R be a ring. An R-module M is said to be noetherian if whenever M1, M2, ... is a sequence of R-submodules of M with
M1 ⊆ M2 ⊆ ...
then there there exists a positive integer n such that Mm = Mn for every m ≥ n.

Noetherian is the mathematical dual of artinian. In a noetherian module, each submodule Mi is contained in (rather than contained by) the submodule Mi+1. Eventually the sequence of submodules becomes stationary. In an analogous situation to that of the photograph Artinian, this is represented by the matryoshka dolls eventually (as we move from left to right) becoming constant in size.

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