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ARTINIAN RINGS AND THE H-CONDITION

Published online by Cambridge University Press:  24 July 2006

P. F. SMITH  and
A. R. WOODWARD
P. F. SMITH
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow, G12 8QW, United Kingdompfs@maths.gla.ac.uk, aw@maths.gla.ac.uk
A. R. WOODWARD
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow, G12 8QW, United Kingdompfs@maths.gla.ac.uk, aw@maths.gla.ac.uk
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Abstract

It is proved that a ring $R$ is right Artinian if and only if, for each countably generated right $R$-module $M$, there exists a finite subset $F$ of $M$ such that the annihilator of $M$ in $R$ equals the annihilator of $F$ in $R$.

Keywords

16P20
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 4 , August 2006 , pp. 571 - 574
Copyright
The London Mathematical Society 2006

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