Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532120140701Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity65826799ENHanamantagouda P. SankappanavarDepartment of Mathematics, State University of New York, New Paltz, NY 12561Journal Article20140510This 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 $mathbf{RDQDStSH_1}$ 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 $mathbf{RDQDStSH_1}$-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 $mathbf{RDQDStSH_1}$. The paper concludes with some open problems for further investigation.https://cgasa.sbu.ac.ir/article_6799_7ce60a297db56c047a8e3b9e503e48ee.pdf