A Note on Regular De Morgan Semi-Heyting Algebras
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...
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| Format: | Article |
| Language: | English |
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De Gruyter
2016-09-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | http://www.degruyter.com/view/j/dema.2016.49.issue-3/dema-2016-0021/dema-2016-0021.xml?format=INT |
| Summary: | 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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| ISSN: | 0420-1213 2391-4661 |