Bouligand-Severi $k$-tangents and strongly semisimple MV-algebras

TL;DR

This paper characterizes strongly semisimple MV-algebras using a geometric concept called Bouligand-Severi $k$-tangents, generalizing classical tangents to higher dimensions.

Contribution

It provides a new geometric characterization of strongly semisimple MV-algebras through Bouligand-Severi $k$-tangents, extending classical tangent concepts.

Findings

Geometric characterization of strongly semisimple MV-algebras

Introduction of Bouligand-Severi $k$-tangents as a generalization

Connection between algebraic properties and geometric structures

Abstract

An algebra $A$ is said to be strongly semisimple if every principal congruence of $A$ is an intersection of maximal congruences. We give a geometrical characterisation of strongly semisimple MV-algebras in terms of Bouligand-Severi $k$-tangents. The latter are a $k$-dimensional generalisation of the classical Bouligand-Severi tangents.