On transfer homomorphisms in commutative rings with zero-divisors

We study the arithmetic of monoids of regular elements of commutative rings with zero-divisors. Our focus is on Krull rings and on some of their generalizations (such as weakly Krull rings and C-rings). We establish sufficient conditions for a subring R of a Krull ring D guaranteeing that the inclusion R•,→D• of the respective monoids of regular elements is a transfer homomorphism. The arithmetic of the Krull monoid D• is well studied and the existence of a transfer homomorphism implies that R• and D• share many arithmetic properties.