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- W2317384085 abstract "The aim of this note is to study the class group of a central Ω-Krull ring and to determine in some cases whether a twisted (semi) group ring is a central Ω-Krull ring. In [ 8 ] we defined an Ω-Krull ring as a generalization of a commutative Krull domain. In the commutative theory, the class group plays an important role. In the second and third section, we generalize some results to the noncommutative case, in particular the relation between the class group of a central Ω-Krull ring and the class group of a localization. Some results are obtained in case the ring is graded. Theorem 3.2 establishes the relation between the class group and the graded class group. In particular, in the P.I. case we obtain that the class group is equal to the graded class group. As a consequence of a result on direct limits of Ω-Krull rings, we are able to derive a necessary and sufficient condition in order that a polynomial ring R [( X i ) i ∊ I ] ( I may be infinite) is a central Ω-Krull ring." @default.
- W2317384085 created "2016-06-24" @default.
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- W2317384085 date "1984-04-01" @default.
- W2317384085 modified "2023-10-01" @default.
- W2317384085 title "On Central Ω-Krull Rings and their Class Groups" @default.
- W2317384085 doi "https://doi.org/10.4153/cjm-1984-014-1" @default.
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