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2016•DOAJ (DOAJ: Directory of Open Access Journals)Open access

A Note on Regular De Morgan Semi-Heyting Algebras

Hanamantagouda P. Sankappanavar

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Abstract

The purpose of this note is two-fold. Firstly, we prove that the variety RDMSH1 of regular De Morgan semi-Heyting algebras of level 1 satisfies Stone identity and present (equational) axiomatizations for several subvarieties of RDMSH1. Secondly, using our earlier results published in 2014, we give a concrete description of the lattice of subvarieties of the variety RDQDStSH1 of regular dually quasi-De Morgan Stone semi- Heyting algebras that contains RDMSH1. Furthermore, we prove that every subvariety of RDQDStSH1, and hence of RDMSH1, has Amalgamation Property. The note concludes with some open problems for further investigation.

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What this paper is about

The purpose of this note is two-fold. Firstly, we prove that the variety RDMSH1 of regular De Morgan semi-Heyting algebras of level 1 satisfies Stone identity and present (equational) axiomatizations for several subvarieties of RDMSH1. Secondly, using our earlier results published in 2014, we give a concrete description of the lattice of subvarieties of the variety RDQDStSH1 of regular dually quasi-De Morgan Stone semi- Heyting algebras that contains RDMSH1. Furthermore, we prove that every subvariety of RDQDStSH1, and hence of RDMSH1, has Amalgamation Property. The note concludes with some open problems for further investigation.

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Available abstract

The purpose of this note is two-fold. Firstly, we prove that the variety RDMSH1 of regular De Morgan semi-Heyting algebras of level 1 satisfies Stone identity and present (equational) axiomatizations for several subvarieties of RDMSH1. Secondly, using our earlier results published in 2014, we give a concrete description of the lattice of subvarieties of the variety RDQDStSH1 of regular dually quasi-De Morgan Stone semi- Heyting algebras that contains RDMSH1. Furthermore, we prove that every subvariety of RDQDStSH1, and hence of RDMSH1, has Amalgamation Property. The note concludes with some open problems for further investigation.

Key concepts: Mathematics, Variety (cybernetics), Pure mathematics, Heyting algebra, Algebra over a field, Statistics

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