Solution of Finite Cauchy difference equations on Free Abelian Group
Main Article Content
Abstract
Let (X, .) be a semigroup, (Y, +) an abelian group and g:X→Y. The first and second order Cauchy differences of g are D1g (a,b) = g (ab) − g (a) − g (b), D2g (a,b,c) = g (abc) – g (ab) – g(bc) − g (ac)+ g(a)+ g (b)+ g (c). Finite order Cauchy differences Dnf are defined recursively. In the case of Y = Z, a ring where multiplication is distributive over addition, we show that functions g : X® Z with finite Cauchy differences are closed under multiplication. The equation Dng = 0 is considered for finite abelian groups
Article Details
Issue
Section
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
Notices:
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.