On transfer homomorphisms in commutative rings with zero-divisors

Key Points

• A transfer homomorphism exists when sufficient conditions are met for subrings in Krull rings, and thus R• shares properties with D•.
• The study focuses on Krull rings and their generalizations, exploring the arithmetic of monoids of regular elements in rings.
• Establishing connections between R• and D• leads to similarities in their arithmetic properties, enhancing our understanding of ring structure.
• The findings expand the known relationships between various types of rings, particularly in the context of zero-divisors.

Abstract