Abstract
Let R be a commutative integral domain with field of fractions F and let Q be a finite-dimensional central simple F-algebra. If R is a Prüfer domain then it is still unknown whether or not R can be extended to a Prüfer order in Q in the sense of Alajbegović and Dubrovin (J. Algebra, 135: 165–176, 1990). In this paper we investigate a more general class of rings which we call rings of Prüfer type and we will prove an extension theorem for these rings. Under special assumptions this result also leads to an extension theorem for certain Prüfer domains.
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Dedicated to Günter Törner on his sixtieth birthday.
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Gräter, J. Extending Rings of Prüfer Type in Central Simple Algebras. Algebr Represent Theor 10, 315–331 (2007). https://doi.org/10.1007/s10468-007-9046-5
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DOI: https://doi.org/10.1007/s10468-007-9046-5