Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity

This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, that the variety mathbfRDQDStSH1 of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1 is the join of the variety generated by the twenty 3-element mathbfRDQDStSH1-chains and the variety of dually quasi-De Morgan Boolean semi-Heyting algebras--the latter is known to be generated by the expansions of the three 4-element Boolean semi-Heyting algebras. As consequences of our main theorem, we present (equational) axiomatizations for several subvarieties of mathbfRDQDStSH1 . The paper concludes with some open problems for further investigation.