Core of an ideal in Prüfer domains

Abstract

This paper contributes to the study of the core of an ideal in integral domains. Our aim is to develop explicit formulas for the core in various classes of Prüfer domains. We pay particular attention to relevant ideal-theoretic notions such as stability, invertibility, and h-local property. We also provide decomposition results for the core of an ideal in integral domains with effectual ramifications to Prüfer domains. All main results are illustrated with original examples, where we explicitly compute the core. We also provide counter-examples to test the limits of the assumptions used in the main results.