On generalized cocycle equations
type: Item
instance of: scholarly article
title: On generalized cocycle equations
zbMATH Open document ID: 0801.39008
DOI: 10.1007/BF01833999
published in: Aequationes Mathematicae
publication date: 1994-11-27T00:00:00Z
full work available at URL: https://eudml.org/doc/137541
review text: The cocycle equation \(F(x + y,z) + F(x,y) = F(x,y + z) + F(y,z)\) is generalized to \(F_ 1(x + y,z) + F_ 2 (y + z,x) + F_ 3 (z + x,y) + F_ 4 (x,y) + F_ 5 (y,z) + F_ 6 (z,x) = 0\), where all the \(F_ i\) are unknown functions mapping the Cartesian product of an abelian group into a vector space over the rationals. The general solution is found and proofs are essentially based on some results on Cauchy differences of higher orders obtained by the authors and \textit{K. J. Heuvers} [ibid. 42, No. 2/3, 137-153 (1991; Zbl 0744.39003)].
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 493235
zbMATH Keywords: cocycle equation
zbMATH Keywords: abelian group
zbMATH Keywords: vector space
zbMATH Keywords: Cauchy differences
author: Bruce Ebanks
author: Che Tat Ng
reviewed by: Bogdan A. Choczewski
MaRDI profile type: Publication
cites work: Q3786871
cites work: On Cauchy differences of all orders
cites work: Some Functional Equations in Groups and Rings.
cites work: Q5682962
cites work: Representation for measures of information with the branching property
OpenAlex ID: W4205275025
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description: scientific article; zbMATH DE number 493235