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# Hopkins theorem

###### Theorem 1.

If a ring with identity is left Artinian then it is left Noetherian.

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

16P20*no label found*16P40

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## Comments

## hopkin's theorem

I would like an outline of the proof

## hopkins theorem

An outline of a proof would be interesting.

## hopkins theorem

add the statement that every prime ideal is maximal after Noetherian.

## hopkins theorem

add to statement of theorem if and only if it is noetherian and every

prime ideal is maximal.

## hopkins theorem

A ring R with identity is left artinian if and only if it is left noetherian and every prime ideal is a maximal ideal.

## hopkins theorem

A ring R with identity is artinian if and only if it is noetherian and every prime ideal is a maximal ideal