2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150803Noncommutative lattices have been recently used as finite topological approximations in quantum physical models. As a first step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their $K$-theory. We shall do it algebraically, by studying the algebraic $K$-theory of the associated algebras of `continuous functions' which turn out to be noncommutative approximately finite dimensional (AF) $C^*$-algebra . We also work out several examples.25 pages, latexQuantum AlgebraHigh Energy Physics - Theorytext