Kronecker function rings and Prüfer extension

By Lokendra Paudel

8 November 2019

Let R be a subring of S. The classical Kronecker function ring when R is a domain and S its quotient field associates to the domain R a Bezout domain (that is, a domain in which every finitely generated ideal is principal). Knebusch and Kaiser introduce a notion of star operation ★ on the commutative ring extension RS and generalize the concept of Kronecker function ring Kr1(★) from integral domains to commutative ring extensions. We introduce a new ring Kr2(★) which is a subring of Kr1(★) and we will show with an example that Kr1(★) ≠ Kr(★). We also discuss the properties of ring extensions using the star operation ★ and in particular, we focus on the case where RS is a Prüfer extension. Joint work with Simplice Tchamna (Georgia College & State University).