TY - JOUR
ID - 6483
TI - Dually quasi-De Morgan Stone semi-Heyting algebras I. Regularity
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Sankappanavar, Hanamantagouda P.
AD - Department of Mathematics, State University of New York, New Paltz, NY 12561
Y1 - 2014
PY - 2014
VL - 2
IS - 1
SP - 47
EP - 64
KW - Regular dually, quasi-De Morgan, semi-Heyting algebra of level 1
KW - dually
pseudocomplemented semi-Heyting algebra
KW - De Morgan semi-Heyting
algebra
KW - strongly blended dually quasi-De Morgan Stone semi-Heyting algebra
KW - discriminator variety
KW - simple
KW - directly indecomposable
KW - subdirectly
irreducible
KW - equational base
DO -
N2 - 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.
UR - https://cgasa.sbu.ac.ir/article_6483.html
L1 - https://cgasa.sbu.ac.ir/article_6483_be76f661bc06e437558fec3ecd0c6f15.pdf
ER -