Congruences on the monoid of monotone injective partial selfmaps of $L_n{\times }_{\mathrm{lex}}\mathbb{Z}$ with co-finite domains and images

Abstract

We study congruences of the semigroup $\mathcal{I}\mathcal{O}{}_{\infty }({\mathbb{Z}}_{\mathrm{lex}}^n)$ of monotone injective partial selfmaps of the set of $L_n{\times }_{\mathrm{lex}}\mathbb{Z}$ having co-finite domain and image, where $L_n{\times }_{\mathrm{lex}}\mathbb{Z}$ is the lexicographic product of $n$-elements chain and the set of integers with the usual linear order. The structure of the sublattice of congruences on $\mathcal{I}\mathcal{O}{}_{\infty }({\mathbb{Z}}_{\mathrm{lex}}^n)$ which contain in the least group congruence is described.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1311.6175