Modular lattices of finite length (Part A)

TL;DR

This paper introduces Part A of a series on modular lattices of finite length, covering known material with some new proofs and concepts, and sets the stage for subsequent parts that will include deep results from notable researchers.

Contribution

It provides a fairly final version of Part A, including a new short proof of distributivity of congruence lattices and introduces the concept of point-splitting.

Findings

Short proof of distributivity of congruence lattices

Introduction of the concept of point-splitting

Treatment of deep results from Herrmann and Wille in English

Abstract

This is Part A of four Parts dedicated to modular lattices of finite length. It builds on 1992 notes of the author (available on ResearchGate), and in so doing heeds a wish of the late Gian-Carlo Rota. Part A is in fairly final form and mainly features known material, exceptions being a short proof of the distributivity of congruence lattices of lattices, as well as the concept of a point-splitting (which applies to arbitrary partial linear spaces). The planned content of Parts B,C,D is given in the introduction of Part A. Suffice it to say that deep results from C.Herrmann and R.Wille will be treated in English for the first time. All of this (even Part A) is work in process and comments/contributions are welcome.