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A Condition for Artinian Rings to be Noetherian
Published online by Cambridge University Press: 20 November 2018
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Throughout this paper the word “Artinian (Noetherian) ring” means an associative ring with minimum (maximum) condition on left ideals. According to C. Hopkins, an Artinian ring is Noetherian if it contains a left or right identity [3, p. 728]. However we shall consider Artinian rings without the assumption of existence of such an identity, and the theorem of Hopkins will be reproved.
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- Copyright © Canadian Mathematical Society 1978
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