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.

局部实Riesz空间上的全格收敛是拓扑，顺序和相对均匀收敛的抽象。我们研究了完全收敛的四个修改$\mathbb{C}$在Riesz空间上。第一个产生顺序收敛$\mathbb{SC}$。第二个绝对$\mathbb{C}$-收敛并推广绝对弱收敛。第三个修改是无限的$\mathbb{C}$-收敛，并概括了文献中最近研究的各种无界收敛。最后一个适用于任何时候$\mathbb{C}$ 是可交换的完全收敛 $升$-代数并产生乘法修改 $\mathbb{mc}$ 的 $\mathbb{C}$。我们研究全格收敛的一般性质，着重于普遍完备的Riesz空间和Archimedean$F$-代数。本文中的技术和结果统一并扩展了最近关于无界收敛的文献中开发和获得的那些技术和结果。