  We 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 $K[[t^2, t^3]]$.
