The core of an ideal $I$ is the intersection of all reductions of $I$. We prove that the core behaves well under extension to the trivial extension. Also, we describe the core as a colon ideal of a power of any reduction and a power $I$, for a class of ideals $I$ in Cohen-Macaulay rings.
"The core of an ideal in Cohen-Macaulay rings." J. Commut. Algebra 10 (2) 163 - 170, 2018. https://doi.org/10.1216/JCA-2018-10-2-163