Extending Rings of Prüfer Type in Central Simple Algebras

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 Prufer domain then it is still unknown whether or not R can be extended to a Prufer order in Q in the sense of Alajbegovic and Dubrovin (J. Algebra, 135: 165–176, 1990). In this paper we investigate a more general class of rings which we call rings of Prufer type and we will prove an extension theorem for these rings. Under special assumptions this result also leads to an extension theorem for certain Prufer domains.