How to extend closure and interior operations to more modules (Q6619981)

The authors give a unified approach for different notions of integral closure of modules (Rees integral closure [\textit{D. Rees}, Math. Proc. Camb. Philos. Soc. 101, 431--449 (1987; Zbl 0628.13004)], Eisenbud-Huneke-Ulrich integral closure [\textit{D. Eisenbud} et al., Proc. Am. Math. Soc. 131, No. 3, 701--708 (2003; Zbl 1038.13002)], and liftable integral closure defined by \textit{N. Epstein} and \textit{B. Ulrich} [``Liftable integral closure'', Preprint, \url{arXiv:1309.6966}]) via the pair operations they introduced earlier [\textit{N. Epstein} et al., J. Pure Appl. Algebra 227, No. 4, Article ID 107256, 33 p. (2023; Zbl 1502.13060)]. They established the cofunctoriality of the pair operations. They then deduced different versions of integral closure of modules.