Journal ArticleDOI
The divisor class group of a semigroup ring
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The divisor class group of a semigroup ring was studied in this article, where the authors propose a semidefinite version of the class group for semigroup rings.Abstract:
(1980). The divisor class group of a semigroup ring. Communications in Algebra: Vol. 8, No. 5, pp. 467-476.read more
Citations
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The isomorphism problem for commutative monoid rings
TL;DR: In this paper, the essentially final positive answer to the isomorphism problem for monoid rings of submonoids of Zr is obtained, which means that the underlying monoid is shown to be determined by the corresponding monoid ring.
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The local class group of a Krull domain
TL;DR: The local class group of a Krull domain A is the quotient group G(A) = CI(A)/Pic(A), where A is locally factorial if and only if A = 0.
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Monoids of IG-type and maximal orders
Isabel Goffa,Eric Jespers +1 more
TL;DR: In this article, it was shown that finitely generated monoids S of IG-type are epimorphic images of monoids of I-type and their algebras K(S) are Noetherian and satisfy a polynomial identity.
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Submonoids of Polycyclic-by-Finite Groups and their Algebras
Eric Jespers,Jan Okniński +1 more
TL;DR: In this article, the authors describe noetherian semigroup algebras K[S] of submonoids S of polycyclic-by-finite groups over a field K and show that they are finitely presented and also are Jacobson rings.
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Locally factorial integral domains
D. D. Anderson,David F. Anderson +1 more
TL;DR: In this paper, it was shown that a locally factorial integral domain R which is not quasilocal is a Krull domain and R, is factorial for each maximal ideal M of R.
References
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Book
The Divisor Class Group of a Krull Domain
TL;DR: Danilov's results as discussed by the authors show that every Abelian group is an Ideal Class Group and every class of Dedekind Domains is an ideal class group of a Krull ring.
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Every abelian group is a class group.
TL;DR: In this article, it was shown that the class group of a Dedekind domain is always a homomorphic image of that of a Krull domain A and that if one of the classes of B are eliminated from the intersection representing B, it would also be eliminable from that representing A.
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Graded krull domains
TL;DR: In this paper, the authors studied Krull domains graded by an arbitrary torsionless grading monoid г and gave necessary and sufficient conditions for A[A] to be a Krull domain and showed that C1(A) is generated by the classes of the homogeneous height-one prime ideals of A.
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