Noetherian module：Noetherian and Artinian module ( part
Noetherian and Artinian module ( part
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 ...
Noetherian modules and rings
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This document is written for readers with some basic familiarity with rings, ideals, and modules. For example, the reader should be familiar ...
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 ...
Definition
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Definition 1. M is a Noetherian module if and only if every submodule of M is finitely generated.