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On some questions related to Koethe's nil ideal problem

Part of: Radicals and radical properties of rings

Published online by Cambridge University Press:  13 February 2015

M. A. Chebotar ,
P.-H. Lee  and
E. R. Puczyłowski
M. A. Chebotar
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242, USA ([email protected])
P.-H. Lee
Affiliation:
Department of Mathematics, National Taiwan University and , National Center for Theoretical Sciences, Taipei Office, Taipei 10617, Taiwan ([email protected])
E. R. Puczyłowski
Affiliation:
Institute of Mathematics, University of Warsaw, 02-097 Warsaw, Banacha 2, Poland ([email protected])
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Abstract

We study properties of two-sided and one-sided ideals of A-rings, i.e. rings that are sums of their nil left ideals. We show that the question as to whether one-sided ideals of A-rings are again A-rings is equivalent to the famous Koethe problem. We also obtain some results on another related open problem that asks whether annihilators of elements of non-zero A-rings are non-zero.

Keywords

Koethe problemnil ringsideals

MSC classification

Secondary: 16N40: Nil and nilpotent radicals, sets, ideals, rings 16N80: General radicals and rings
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 1 , February 2016 , pp. 57 - 64
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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