On the periodicity of irreducible elements in arithmetical congruence monoids

Abstract

Arithmetical congruence monoids, which arise in non-unique factorization theory, are multiplicative monoids M a,b consisting of all positive integers n satsfying n ≡ a mod b. In this paper, we examine the asymptotic behavior of the set of irreducible elements of M a,b , and characterize in terms of a and b when this set forms an eventually periodic sequence.