  The full lattice convergence on a locally solid Riesz space is an abstraction
of the topological, order, and relatively uniform convergences. We investigate
four modifications of a full convergence $\mathbb{c}$ on a Riesz space. The
first one produces a sequential convergence $\mathbb{sc}$. The second makes an
absolute $\mathbb{c}$-convergence and generalizes the absolute weak
convergence. The third modification makes an unbounded $\mathbb{c}$-convergence
and generalizes various unbounded convergences recently studied in the
literature. The last one is applicable whenever $\mathbb{c}$ is a full
convergence on a commutative $l$-algebra and produces the multiplicative
modification $\mathbb{mc}$ of $\mathbb{c}$. We study general properties of full
lattice convergence with emphasis on universally complete Riesz spaces and on
Archimedean $f$-algebras. The technique and results in this paper unify and
extend those which were developed and obtained in recent literature on
unbounded convergences.
