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On a functional equation related to projections of abelian groups

Rätz, Jürg

In: aequationes mathematicae, 2005, vol. 70, no. 3, p. 279-297

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    Titel
    • On a functional equation related to projections of abelian groups
    Autor
    • Rätz, Jürg. Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012, Bern, Switzerland
    Dokumententyp
    • Postprint
    Sprache
    • Englisch
    Veröffentlicht in
    • aequationes mathematicae, 2005, vol. 70, no. 3, p. 279-297. Birkhäuser-Verlag; www.birkhauser.ch
    Andere elektronische Ausgabe
    OAI-PMH-ID
    • oai:doc.rero.ch:321911
    Summary
    Summary.: For an abelian group (G,+,0) we consider the functional equation (1) $$f:G \to G,\;f(x + y + f(y)) = f(x) + 2f(y)\quad (\forall x,y \in G),$$ most times together with the condition f(0)=0. A solution of (1) is always idempotent. Our main question is as to whether it must be additive, i.e., a projection of the abelian group G