Definition:Artinian Module

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Let $A$ be a commutative ring with unity.

Let $M$ be an $A$-module

Then $M$ is a Artinian module if either of the following conditions hold:

$(1): \quad$ $M$ satisfies the descending chain condition on submodules
$(2): \quad$ $M$ satisfies the minimal condition on submodules.

Also see

Source of Name

This entry was named for Emil Artin.