On extending Pruefer rings in central simple algebras
- We give an example of a commutative Prufer domain R with field of fractions F and a quaternion division algebra D with centre F such that R cannot be extended to a Prufer order in D in the sense of [AD]. This shows, that a general extension theorem for Prufer orders in central simple algebras does not exist and finally answers a question given in [MMU]. Moreover, in our example R is a Bezout domain which is the intersection of a countable number of (non-discrete) real valuation rings.
