2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168921We investigate the algebraic structure on the set of closure operations of a ring. We show the set of closure operations is not a monoid under composition for a discrete valuation ring. Even the set of semiprime operations over a DVR is not a monoid; however, it is the union of two monoids, one being the left but not right act of the other. We also determine all semiprime operations over the ring $K[[t^2, t^3]]$.Commutative Algebratext