Noetherian module：Noetherian modules and rings

Noetherian module

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In abstract algebra, a Noetherian module is a module that satisfies the ascending chain condition on its submodules, where the submodules are partially ...

NOETHERIAN MODULES 1. Introduction In a finite

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... Noetherian module is a module that is not finitely generated. For example, an infinite-dimensional vector space over a field F is a non-Noetherian F-module,.

Noetherian Module

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A module M is Noetherian if it obeys the ascending chain condition with respect to inclusion, i.e., if every set of increasing sequences of submodules ...

III Topic

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A Noetherian module need not be Artinian. 7. There are modules which are neither Artinian nor Noetherian. Definition : A ring R is called a left noetherian ring ...

Noetherian

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Let $R$ be a ring and $M$ a left $R$ -module. Then we say that $M$ is a Noetherian module if it satisfies the following property, known as the ascending ...

6. Artinian and Noetherian modules

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A module is both Artinian and Noetherian if and only if it has finite length. Pertaining to the Noetherian condition alone, we make two more observations: • Any ...

Noetherian and Artinian module ( part

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Definition

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Definition 1. M is a Noetherian module if and only if every submodule of M is finitely generated.