(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 5, PAGES 85-92

## On quasiorder lattices and topology lattices of algebras

A. V. Kartashova

Abstract

View as HTML     View as gif image

In this paper, it is shown that the dual $\mathop \left\{\widetilde \left\{\mathrm \left\{Qord\right\}\right\}\right\}\mathfrak A$ of the quasiorder lattice of any algebra $\mathfrak A$ is isomorphic to a sublattice of the topology lattice $\Im \left(\mathfrak A\right)$. Further, if $\mathfrak A$ is a finite algebra, then $\mathop \left\{\widetilde \left\{\mathrm \left\{Qord\right\}\right\}\right\}\mathfrak A \cong \Im \left(\mathfrak A\right)$. We give a sufficient condition for the lattices $\mathop \left\{\widetilde \left\{\mathrm \left\{Con\right\}\right\}\right\}\mathfrak A$, $\mathop \left\{\widetilde \left\{\mathrm \left\{Qord\right\}\right\}\right\}\mathfrak A$, and $\Im \left(\mathfrak A\right)$ to be pairwise isomorphic. These results are applied to investigate topology lattices and quasiorder lattices of unary algebras.

Location: http://mech.math.msu.su/~fpm/eng/k08/k085/k08505h.htm