Geodesic
Krull Semigroups and Divisor Class Groups
Canadian journal of mathematics, Tome 33 (1981) no. 6, pp. 1459-1468

Voir la notice de l'article provenant de la source Cambridge University Press

R. Matsuda has shown that a group ring is a Krull domain if and only if the coefficient ring is a Krull domain and the group is a torsion-free abelian group satisfying the ascending chain condition (ace) on cyclic subgroups [6]. D. F. Anderson has used this to obtain a partial determination of when a semigroup ring is a Krull domain, and under certain circumstances to describe the divisor class group of such a ring ([1], [2]). Using some of Anderson's techniques, but taking a different approach, we arrive at a complete answer of a different nature to these questions. We call a semigroup satisfying the major new conditions arising a Krull semigroup, and define its divisor class group.In particular, every abelian group is the divisor class group of such a ring, and it follows that every abelian group is the divisor class group of a quasi-local ring, which seems to be a new result. 
Krull Semigroups and Divisor Class Groups. Canadian journal of mathematics, Tome 33 (1981) no. 6, pp. 1459-1468. doi: 10.4153/CJM-1981-112-x
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[7] 7. Samuel, P., Lecture on unique factorization domains, Tata Institute, Bombay (1964). Google Scholar

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