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Rings whose additive endomorphisms are ring endomorphisms

Published online by Cambridge University Press:  17 April 2009

Gary Birkenmeier  and
Henry Heatherly
Gary Birkenmeier
Affiliation:
Department of Mathematics, University of Southwestern, Louisiana Lafayette, Louisiana 70504, United States of America
Henry Heatherly
Affiliation:
Department of Mathematics, University of Southwestern, Louisiana Lafayette, Louisiana 70504, United States of America
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Abstract

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A ring R is said to be an AE-ring if every additive endomorphism is a ring endomorphism. In this paper further steps are made toward solving Sullivan's Problem of characterising these rings. The classification of AE-rings with. R3 ≠ 0 is completed. Complete characterisations are given for AE-rings which are either: (i) subdirectly irreducible, (ii) algebras over fields, or (iii) additively indecomposable. Substantial progress is made in classifying AE-rings which are mixed – the last open case – by imposing various finiteness conditions (chain conditions on special ideals, height restricting conditions). Several open questions are posed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 1 , August 1990 , pp. 145 - 152
Copyright
Copyright © Australian Mathematical Society 1990

References

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