On the asymptotic behaviour of the number of distinct factorizations into irreducibles

Abstract

For an integral domain R and a non-zero non-unitaεR we consider the number of distinct factorizations of aⁿ into irreducible elements of R for large n. Precise results are obtained for Krull domains and certain noetherian domains. In fact, we prove results valid for certain classes of monoids which then apply to the above-mentioned classes of domains.