On Generalization of Modular Lattices

Abstract

We introduce the concepts of dually balanced lattices and \(M\)-lattices and provide some basic properties of these classes of lattices. Both classes can be viewed as generalizations of the well-known class of modular lattices. In particular, we obtain analogues of the Kurosh-Ore theorem for dually balanced lattices and the Jordan-Hölder theorem for \(M\)-lattices. Furthermore, we investigate the behaviour of several invariants, including the hollow dimension and the Kurosh-Ore dimension in dually balanced lattices, as well as the maximal dimension in \(M\)-lattices.