Manfred Dugas, Shalom Feigelstock

Research output: Contribution to journalArticlepeer-review


E-rings are a well known notion in the theory of abelian groups. They are those rings R such that End (R+), the ring of endomorphisms of the additive group of R, is as small as possible, i.e. End (R+)=Rℓ, where Rℓ={x↦ax:a∈R}(. We generalize the notion of E-rings by calling a ring R an almost- E-ring, or AE-ring for short, if End (R+) is a radical extension of Rℓ, i.e. for each φ∈End (R+) there is some natural number n such that φn∈Rℓ. We will show that this notion does not lead to a new class of rings. It turns out that all AE-rings are actually E-rings. Our proof utilizes Herstein’s Hypercenter Theorem.

Original languageEnglish
Pages (from-to)239-246
Number of pages8
JournalRendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
StatePublished - 2004

Bibliographical note

Publisher Copyright:
© 2004, Universita di Padova. All rights reserved.


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