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Rings whose additive endomorphisms are ring endomorphisms

Published online by Cambridge University Press:  17 April 2009

Manfred Dugas ,
Jutta Hausen  and
Johnny A. Johnson
Manfred Dugas
Affiliation:
Baylor University, Waco TX 76798-7328, United States of America
Jutta Hausen
Affiliation:
University of Houston, Houston TX 77204-3476, United States of America
Johnny A. Johnson
Affiliation:
University of Houston, Houston TX 77204-3476, 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 endomorphism of its additive group R+ is a ring endomorphism. Clearly, the zero ring on any abelian group is an AE-ring. In a recent article, Birkenmeier and Heatherly characterised the so-called standard AE-lings, that is, the non-trivial AE-rings whose maximal 2-subgroup is a direct summand. The present article demonstrates the existence of non-standard AE-rings. Four questions posed by Birkenmeier and Heatherly are answered in the negative.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 1 , February 1992 , pp. 91 - 103
Copyright
Copyright © Australian Mathematical Society 1992

References

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