Algebraic structures from the point of view of complete multiplicative lattices

TL;DR

This paper extends recent results on multiplicative lattices from groups to more general algebraic structures like braces, broadening their applicability in algebra.

Contribution

It proves that key properties of multiplicative lattices hold beyond groups, enabling their use in a wider range of algebraic systems.

Findings

Results apply to normal subgroup lattices of groups

Results extend to more general multiplicative lattices

Applicable to algebraic structures like braces

Abstract

General results on multiplicative lattices found recently by Facchini, Finocchiaro and Janelidze have been studied in the particular case of groups by Facchini, de Giovanni and Trombetti. In this paper we prove that these results hold not only for the multiplicative lattices of all normal subgroups of a group, but also for much more general multiplicative lattices. Therefore they can be applied to other algebraic structures, for instance to braces.