  We carry on a more detailed investigation of the composition of locally solid
convergences as introduced in [BCTvdW24], as well as the corresponding notion
of idempotency considered in [Bil23]. In particular, we study the interactions
between these two concepts and various operations with convergences. We prove
associativity of the composition and show that the adherence of an ideal with
respect to an idempotent convergence is equal to its closure. Some results from
[KT18] about unbounded modification of locally solid topologies are generalized
to the level of locally solid idempotent convergences. A simple application of
the composition allows us to answer a question from [BCTvdW24] about minimal
Hausdorff locally solid convergences. We also show that the weakest Hausdorff
locally solid convergence exists on an Archimedean vector lattice if and only
if it is atomic.
