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On extending Prüfer rings in central simple algebras
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Joachim Gräter
Veröffentlicht/Copyright:
30. Januar 2009
Abstract
We give an example of a commutative Prüfer domain R with field of fractions F and a quaternion division algebra D with centre F such that R cannot be extended to a Prüfer order in D in the sense of [Alajbegović and Dubrovin, J. Algebra 135: 165–176, 1990]. This shows, that a general extension theorem for Prüfer orders in central simple algebras does not exist and finally answers a question given in [Marubayashi, Miyamoto, Ueda, Non-commutative Valuation Rings and Semihereditary Orders. K-Monographs in Mathematics 3, Kluwer, 1997]. Moreover, in our example R is a Bézout domain which is the intersection of a countable number of (non-discrete) real valuation rings.
Received: 2007-01-30
Published Online: 2009-01-30
Published in Print: 2009-January
© de Gruyter 2009
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Artikel in diesem Heft
- Central extensions of rank 2 groups and applications
- Generating abelian groups by addition only
- Intrinsic ultracontractivity for non-symmetric Lévy processes
- K-Theory of non-linear projective toric varieties
- Wakamatsu tilting modules with finite FP-injective dimension
- The catenary and tame degree of numerical monoids
- On extending Prüfer rings in central simple algebras
- Geometry of the cone of positive quadratic forms
Artikel in diesem Heft
- Central extensions of rank 2 groups and applications
- Generating abelian groups by addition only
- Intrinsic ultracontractivity for non-symmetric Lévy processes
- K-Theory of non-linear projective toric varieties
- Wakamatsu tilting modules with finite FP-injective dimension
- The catenary and tame degree of numerical monoids
- On extending Prüfer rings in central simple algebras
- Geometry of the cone of positive quadratic forms
