A note on regular De Morgan semi-Heyting algebras

TL;DR

This paper investigates the algebraic structure of regular De Morgan semi-Heyting algebras, proving they satisfy Stone identity, providing axiomatizations for subvarieties, and analyzing the lattice of subvarieties with the Amalgamation Property.

Contribution

It offers new axiomatizations for subvarieties of regular De Morgan semi-Heyting algebras and describes the subvariety lattice of related algebraic structures.

Findings

RDMSH1 satisfies Stone identity

Axiomatizations for subvarieties of RDMSH1

All subvarieties of RDQDStSH1 have Amalgamation Property

Abstract

The purpose of this note is two-fold. Firstly, we prove that the variety RDMSH1 of regular De Morgan semi-Heyting algebras of level 1 satisfies Stone identity and present (equational) axiomatizations for several subvarieties of RDMSH1. Secondly, we give a concrete description of the lattice of subvarieties of the variety RDQDStSH1 of regular dually quasi-De Morgan Stone semi-Heyting algebras that contains RDMSH1 . Furthermore, we prove that every subvariety of RDQDStSH1, and hence of RDMSH1, has Amalgamation Property. The note concludes with some open problems for further investigation.