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Functions on semigroups with vanishing finite Cauchy differences.
- Source :
- Aequationes Mathematicae; Feb2016, Vol. 90 Issue 1, p235-247, 13p
- Publication Year :
- 2016
-
Abstract
- Let $${(S,\cdot)}$$ be a semigroup, ( H, +) an abelian group and $${f: S \to H}$$ . The first and second order Cauchy differences of f are Higher order Cauchy differences C f are defined recursively. In the case of H = R, a ring where multiplication is distributive over addition, we show that functions $${f: S\to R}$$ with vanishing finite Cauchy differences are closed under multiplication. The equation C f = 0 is considered for cyclic groups, free abelian groups and other selected quotients of the free groups. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 90
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 113577108
- Full Text :
- https://doi.org/10.1007/s00010-015-0403-x