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On some questions related to Koethe's nil ideal problem

Published online by Cambridge University Press:  13 February 2015

M. A. Chebotar
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242, USA (chebotar@math.kent.edu)
P.-H. Lee
Affiliation:
Department of Mathematics, National Taiwan University and , National Center for Theoretical Sciences, Taipei Office, Taipei 10617, Taiwan (phlee@math.ntu.edu.tw)
E. R. Puczyłowski
Affiliation:
Institute of Mathematics, University of Warsaw, 02-097 Warsaw, Banacha 2, Poland (edmundp@mimuw.edu.pl)

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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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