%0 Journal Article
%T Dually quasi-De Morgan Stone semi-Heyting algebras I. Regularity
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Sankappanavar, Hanamantagouda P.
%D 2014
%\ 07/01/2014
%V 2
%N 1
%P 47-64
%! Dually quasi-De Morgan Stone semi-Heyting algebras I. Regularity
%K Regular dually, quasi-De Morgan, semi-Heyting algebra of level 1
%K dually
pseudocomplemented semi-Heyting algebra
%K De Morgan semi-Heyting
algebra
%K strongly blended dually quasi-De Morgan Stone semi-Heyting algebra
%K discriminator variety
%K simple
%K directly indecomposable
%K subdirectly
irreducible
%K equational base
%R
%X This paper is the first of a two part series. In this paper, we first prove that the variety of dually quasi-De Morgan Stone semi-Heyting algebras of level 1 satisfies the strongly blended $lor$-De Morgan law introduced in cite{Sa12}. Then, using this result and the results of cite{Sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) in the variety of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1. It is shown that there are 25 nontrivial simple algebras in this variety. In Part II, we prove, using the description of simples obtained in this Part, 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 this theorem, we present (equational) axiomatizations for several subvarieties of $mathbf{RDQDStSH_1}$. The Part II concludes with some open problems for further investigation.
%U https://cgasa.sbu.ac.ir/article_6483_be76f661bc06e437558fec3ecd0c6f15.pdf