Volume 24 • Number 1 • 2001   • 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. Full text: PDF