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Halbgruppen mit Divisorentheorie. (Semigroups with divisor theory). (German) Zbl 0698.20054
Let H be a regular commutative semigroup with divisor theory. The author determines first the structure of the quotient group of H, gives a criterion for isomorphism of two such groups and gives necessary and sufficient conditions for the existence of H with given divisor class group and the set of cardinalities of the sets of prime divisors in divisor classes. The remainder of the paper deals with problems concerning the deviation of H from having unique factorization.
Reviewer: W.Narkiewicz

20M14 Commutative semigroups
11R99 Algebraic number theory: global fields
20M15 Mappings of semigroups