Browse Books

This paper concerns the construction of the so-called augmented product codes and augmented product lattices. These are obtained by augmenting product codes or product lattices from certain classes thus obtaining higher dimensional codes or lattices ...

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. ...$\mathcal{}$

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,...$\mathrm{}\mathrm{}$