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Arithmetic Funtions Over Rings with
Zero Divisors Pattira
Ruangsinsap, Vichian Laohakosol and Pattanee Udomkavanich Abstract.
It is well known that the complex-valued arithmetic functions
form a unique factorization domain under addition and
convolution, and so do those functions with values in
other suitable rings. Here we consider instead such functions
with values in a unique factorization ring with zero divisors
and prove that under certain yet similar conditions, they
also form a unique factorization ring with zero divisors.
