1996•Proceedings of the Edinburgh Mathematical SocietyOpen access
On semi-artinian modules and injectivity conditions
John Clark, Patrick F. Smith
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Abstract
It is well known that a module M has finite length if and only if it is semi-artinian and Noetherian or, equivalently, semi-noetherian and artinian. Our main result shows that finite length is often achieved by just assuming that M is semi-artinian, semi-noetherian and has finitely generated socle.
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