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

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Abstract


Abstract. 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
RDQDStSH1 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
RDQDStSH1-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 RDQDStSH1. The paper concludes with some open problems
for further investigation.

Keywords


Regular dually quasi-De Morgan semi-Heyting algebra of level 1, dually pseudocomple- mented semi-Heyting algebra, De Morgan semi-Heyting algebra, strongly blended dually quasi-De Morgan Stone semi-Heyting algebra, discriminator variety, simple, directly i

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References


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