Dedekind semidomains are defined via invertible fractional ideals, with proofs that Noetherian cases equal multiplication semirings, subtractive Noetherian cases equal π-semirings with invertible primes, and subtractive cases have ideals generated by at most two elements.
Algebra Appl., 16(11) (2018), Article ID 1850073 (23 pages)
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Dedekind semidomains
Dedekind semidomains are defined via invertible fractional ideals, with proofs that Noetherian cases equal multiplication semirings, subtractive Noetherian cases equal π-semirings with invertible primes, and subtractive cases have ideals generated by at most two elements.