Abstract
An abelian group G is said to be an E-group if it is the additive group of an E-ring. It is known that G is an E-group if and only if there exists a left E(G)-module isomorphism from G to its endomorphism ring E(G). Groups which are isomorphic to the additive group of their endomorphism rings are called weak E-groups. The purpose of this article is to consider the apparently yet weaker condition that there be a homorphism from G onto the additive group of E(G). Groups satisfying this condition are called EE-groups. The properties of EE-groups are studied and it is shown that they are very similar to E-groups. In fact, it is shown that every EE-group of finite torsion-free rank is a weak E-group, and that for various prominent classes of groups the concepts of EE-group and E-group coincide.
The second author wishes to thank Bar-Ilan University and Hebrew University for their hospitality and support.
The third author acknowledges the hospitality of Bar-Ilan University and of the Hebrew University. He also acknowledges support from the NSERC (Canada).
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Feigelstock, S., Hausen, J., Raphael, R. (1999). Abelian groups mapping onto their endomorphism rings. In: Eklof, P.C., Göbel, R. (eds) Abelian Groups and Modules. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7591-2_18
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DOI: https://doi.org/10.1007/978-3-0348-7591-2_18
Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-7591-2
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