Irreducible Elements in Metric Lattices

TL;DR

This paper generalizes the concept of irreducibility in order lattices equipped with various metrics, analyzing special cases like valuation metrics and addressing open questions from the author's doctoral research.

Contribution

It introduces a natural extension of irreducibility in metric lattices and explores specific metric cases, providing new insights beyond previous work.

Findings

Generalization of irreducibility in metric lattices

Analysis of valuation and other metrics in lattices

Answers to open questions from doctoral research

Abstract

We describe a natural generalization of irreducibility in order lattices with arbitrary metrics. We analyse the special cases of valuation metrics and more general metrics for lattices. This article is mainly based on a part of the author's doctoral thesis, but answers some additional questions.