Core of ideals in integral domains

This paper uses objects and techniques from multiplicative ideal theory to develop explicit formulas for the core of ideals in various classes of integral domains (not necessarily Noetherian). We also investigate the existence of minimal reductions (originally established by Rees and Sally for local Noetherian rings). All results are illustrated by original examples in Noetherian and non-Noetherian settings, where we explicitly compute the core and validate some open questions recently raised in the literature.