Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity
This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, 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 $mat...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2014-07-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | http://www.cgasa.ir/article_6799_7ce60a297db56c047a8e3b9e503e48ee.pdf |
| _version_ | 1818701542378700800 |
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| author | Hanamantagouda P. Sankappanavar |
| author_facet | Hanamantagouda P. Sankappanavar |
| author_sort | Hanamantagouda P. Sankappanavar |
| collection | DOAJ |
| description | This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, 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 our main theorem, we present (equational) axiomatizations for several subvarieties of $mathbf{RDQDStSH_1}$. The paper concludes with some open problems for further investigation. |
| first_indexed | 2024-12-17T15:22:30Z |
| format | Article |
| id | doaj.art-3f0f14f920eb44c88369c3dd81e6f407 |
| institution | Directory Open Access Journal |
| issn | 2345-5853 2345-5861 |
| language | English |
| last_indexed | 2024-12-17T15:22:30Z |
| publishDate | 2014-07-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj.art-3f0f14f920eb44c88369c3dd81e6f4072022-12-21T21:43:21ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612014-07-012165826799Dually quasi-De Morgan Stone semi-Heyting algebras II. RegularityHanamantagouda P. Sankappanavar0Department of Mathematics, State University of New York, New Paltz, NY 12561This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, 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 our main theorem, we present (equational) axiomatizations for several subvarieties of $mathbf{RDQDStSH_1}$. The paper concludes with some open problems for further investigation.http://www.cgasa.ir/article_6799_7ce60a297db56c047a8e3b9e503e48ee.pdfRegular dually quasi-De Morgan semi-Heyting algebra of level 1dually pseudocomplemented semi-Heyting algebraDe Morgan semi-Heyting algebrastrongly blended dually quasi-De Morgan Stone semi-Heyting algebradiscriminator varietysimpledirectly indecomposablesubdirectly irreducibleequational base |
| spellingShingle | Hanamantagouda P. Sankappanavar Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity Categories and General Algebraic Structures with Applications Regular dually quasi-De Morgan semi-Heyting algebra of level 1 dually pseudocomplemented semi-Heyting algebra De Morgan semi-Heyting algebra strongly blended dually quasi-De Morgan Stone semi-Heyting algebra discriminator variety simple directly indecomposable subdirectly irreducible equational base |
| title | Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity |
| title_full | Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity |
| title_fullStr | Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity |
| title_full_unstemmed | Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity |
| title_short | Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity |
| title_sort | dually quasi de morgan stone semi heyting algebras ii regularity |
| topic | Regular dually quasi-De Morgan semi-Heyting algebra of level 1 dually pseudocomplemented semi-Heyting algebra De Morgan semi-Heyting algebra strongly blended dually quasi-De Morgan Stone semi-Heyting algebra discriminator variety simple directly indecomposable subdirectly irreducible equational base |
| url | http://www.cgasa.ir/article_6799_7ce60a297db56c047a8e3b9e503e48ee.pdf |
| work_keys_str_mv | AT hanamantagoudapsankappanavar duallyquasidemorganstonesemiheytingalgebrasiiregularity |