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 |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/dema.2016.49.issue-3/dema-2016-0021/dema-2016-0021.xml?format=INT |
| _version_ | 1818972508660957184 |
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| author | Sankappanavar Hanamantagouda P. |
| author_facet | Sankappanavar Hanamantagouda P. |
| author_sort | Sankappanavar Hanamantagouda P. |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T15:09:23Z |
| format | Article |
| id | doaj.art-ef8b0acefaa047a89a633a4cd985b3fa |
| institution | Directory Open Access Journal |
| issn | 0420-1213 2391-4661 |
| language | English |
| last_indexed | 2024-12-20T15:09:23Z |
| publishDate | 2016-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-ef8b0acefaa047a89a633a4cd985b3fa2022-12-21T19:36:23ZengDe GruyterDemonstratio Mathematica0420-12132391-46612016-09-0149325226510.1515/dema-2016-0021dema-2016-0021A Note on Regular De Morgan Semi-Heyting AlgebrasSankappanavar Hanamantagouda P.0DEPARTMENT OF MATHEMATICS, STATE UNIVERSITY OF NEW YORK, NEW PALTZ, NY 12561, U.S.AThe 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.http://www.degruyter.com/view/j/dema.2016.49.issue-3/dema-2016-0021/dema-2016-0021.xml?format=INTregular De Morgan semi-Heyting algebra of level 1lattice of subvarietiesamalgamation propertydiscriminator varietysimplesubdirectly irreducibleequational base |
| spellingShingle | Sankappanavar Hanamantagouda P. A Note on Regular De Morgan Semi-Heyting Algebras Demonstratio Mathematica regular De Morgan semi-Heyting algebra of level 1 lattice of subvarieties amalgamation property discriminator variety simple subdirectly irreducible equational base |
| title | A Note on Regular De Morgan Semi-Heyting Algebras |
| title_full | A Note on Regular De Morgan Semi-Heyting Algebras |
| title_fullStr | A Note on Regular De Morgan Semi-Heyting Algebras |
| title_full_unstemmed | A Note on Regular De Morgan Semi-Heyting Algebras |
| title_short | A Note on Regular De Morgan Semi-Heyting Algebras |
| title_sort | note on regular de morgan semi heyting algebras |
| topic | regular De Morgan semi-Heyting algebra of level 1 lattice of subvarieties amalgamation property discriminator variety simple subdirectly irreducible equational base |
| url | http://www.degruyter.com/view/j/dema.2016.49.issue-3/dema-2016-0021/dema-2016-0021.xml?format=INT |
| work_keys_str_mv | AT sankappanavarhanamantagoudap anoteonregulardemorgansemiheytingalgebras AT sankappanavarhanamantagoudap noteonregulardemorgansemiheytingalgebras |