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On semi-artinian modules and injectivity conditions

Published online by Cambridge University Press:  20 January 2009

J. Clark  and
P. F. Smith
J. Clark
Affiliation:
Department of Mathematics and StatisticsUniversity of OtagoP. O. Box 56 DunedinNew Zealand E-mail: jclark@maths.otago.ac.nz
P. F. Smith
Affiliation:
Department of MathematicsUniversity of GlasgowUniversity GardensGlasgow G12 8QWScotland E-mail: pfs@maths.gla.ac.uk
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Abstract

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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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 2 , June 1996 , pp. 263 - 270
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

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