Leibniz-Additive Functions on UFD's
Viachaslau I. Murashka
Faculty of Mathematics and Technologies of Programming
Gomel State University
Andrey D. Goncharenko and Irina N. Goncharenko
State Educational Establishment "Gymnasium 71"
Recall that an arithmetic function f is called an L-additive
function with respect to a completely multiplicative function h
if f(mn) = f(m)h(n) +
f(n)h(m) holds for all m and
n. We study L-additive functions in the fields of fractions
of unique factorization domains (UFD). In particular, we describe all
L-additive functions over given UFD such that these functions can be
extended to its field of fractions. We find the exact formula for an
L-additive function in the terms of prime elements. For a given L-additive
function f(x) we study the properties of the sequence
and solutions of the equation
f(x) = αx. As corollaries we obtain results
about the arithmetic derivative and partial arithmetic derivatives.
Full version: pdf,
(Concerned with sequences
Received June 12 2020; revised versions received August 22 2020;
August 25 2020.
Published in Journal of Integer Sequences,
October 17 2020.
Journal of Integer Sequences home page