On Generalization of Modular Lattices

Agnieszka Stocka

doi:10.18778/0138-0680.2025.15

Authors

Agnieszka Stocka University of Białystok, Faculty of Mathematics https://orcid.org/0000-0001-5013-278X

DOI:

https://doi.org/10.18778/0138-0680.2025.15

Keywords:

modular lattice, hollow dimension, Kurosh-Ore dimension

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.

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