2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170420We define a closure operation for rings of mixed characteristic and verify that the closure is a ring. We then show that this closure produces a ring with good properties with respect to its Fontaine ring and give an example to show that rings that are not closed in this sense do not satisfy these properties.Commutative Algebra13B22;13K05text