Solution of Finite Cauchy difference equations on Free Abelian Group

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M. Pradeep,Dr. S. Renukadevi

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

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How to Cite
M. Pradeep,Dr. S. Renukadevi. (2023). Solution of Finite Cauchy difference equations on Free Abelian Group. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(2), 1230–1232. https://doi.org/10.17762/turcomat.v11i2.14109
Section
Research Articles