Halter-Koch, Franz On products of additive functions (a third approach). (English) Zbl 0777.12001 Aequationes Math. 45, No. 2-3, 281-284 (1993). Summary: Let \(a_ 1,\dots,a_ s:G\to K\) be additive functions from an abelian group \(G\) into a field \(K\) such that \(a_ 1(g)\cdot \dots \cdot a_ s(g)=0\) for all \(g\in G\). If char\((K)=0\), then it is well known that one of the functions \(a_ j\) has to vanish [cf. the author, L. Reich and J. Schwaiger, Aequationes Math. 45, 83-88 (1993; Zbl 0773.39006)]. We give a new proof of this result and show that, if char\((K)>0\), it is only valid under additional assumptions. Cited in 1 Document MSC: 12E05 Polynomials in general fields (irreducibility, etc.) 15A06 Linear equations (linear algebraic aspects) 39B52 Functional equations for functions with more general domains and/or ranges Keywords:products of additive functions; positive characteristic Citations:Zbl 0773.39006 PDFBibTeX XMLCite \textit{F. Halter-Koch}, Aequationes Math. 45, No. 2--3, 281--284 (1993; Zbl 0777.12001) Full Text: DOI EuDML References: [1] Bourbaki, N.,Algebra, Part I. Hermann, Paris and Addison-Wesley, Reading, MA, 1974. [2] Halter-Koch, F., Reich, L. andSchwaiger, J.,On products of additive functions. Aequatione Math., to appear. [3] Lang, S.,Algebra. Addison-Wesley, Reading, MA, 1965. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.