Arithmetic structure including both unique factorization and Dedekind domains

abstract-algebra ring-theory unique-factorization-domains integral-domain dedekind-domain

Has an algebraic arithmetic structure been defined on integral domains, which would include both Dedekind rings and unique factorization domain with respect to the arithmetic properties, and more specifically with respect to the "unique decomposition" into prime objects?

Prüfer domains are too general and does not seem to provide the arithmetic. Valuations on integral domains are good, but they allow only local arithmetic.


Solution 1:

I’m not clear on what “arithmetic” means here but I’ll suggest the following properties which may help you.

Krull domains generalize both UFDs and Dedekind domains, while atomic domains generalize UFDs by dropping unicity of decomposition.

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