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A residuated lattice is said to be integrally closed if it satisfies the quasiequations  $xy\le x\Rightarrow y\le \mathrm{e}$  and  $yx\le x\Rightarrow y\le \mathrm{e}$, or equivalently, the equations  $x\backslash x\approx \mathrm{e}$  and  $x/x\approx \mathrm{e}$. Every integral, cancellative, or divisible residuated lattice is integrally closed,...$\mathrm{}\mathrm{}$

In this paper, a combination of algebraic and topological methods is applied to obtain new and structural results on Gelfand residuated lattices. It is demonstrated that Gelfand’s residuated lattices strongly tied up with the hull–kernel topology. ...$\mathcal{}$

Skew lattices are one of the most successful non-commutative generalizations of lattices. Motivated by the study of residuation on ordered structures and that of skew Boolean algebras and skew Heyting algebras, in this paper, we ...