Hanamantagouda P. Sankappanavar - Department of Mathematics, State University of New York, New Paltz, NY ۱۲۵۶۱

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 mathbf{RDQDStSH_۱} of regular dually quasi-De Morgan Stone semi-Heyting algebras of level ۱ is the join of the variety generated by the twenty ۳-element mathbf{RDQDStSH_۱}-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 ۴-element Boolean semi-Heyting algebras. As consequences of our main theorem, we present (equational) axiomatizations for several subvarieties of mathbf{RDQDStSH_۱}. The paper concludes with some open problems for further investigation.

Regular dually quasi-De Morgan semi-Heyting algebra of level ۱, dually pseudocomplemented semi-Heyting algebra, De Morgan semi-Heyting algebra, strongly blended dually quasi-De Morgan Stone semi-Heyting algebra, discriminator variety, simple, directly indecomposable, subdirectly irreducible, equational base