Varieties of Regular Pseudocomplemented de Morgan Algebras
| Autor: | Hanamantagouda P. Sankappanavar, M. E. Adams, Júlia Vaz de Carvalho |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Algebra and Number Theory 010102 general mathematics Duality (mathematics) 0102 computer and information sciences Mathematics - Logic Lattice (discrete subgroup) 01 natural sciences Mathematics::Logic Cardinality Computational Theory and Mathematics Chain (algebraic topology) 010201 computation theory & mathematics Simple (abstract algebra) Subdirectly irreducible algebra FOS: Mathematics Geometry and Topology Simple algebra 0101 mathematics Variety (universal algebra) Primary \ 06D30 06D15 03G25 Secondary \ 08B15 06D50 03G10 Logic (math.LO) Mathematics |
| Popis: | In this paper, we investigate the varieties $\mathbf M_n$ and $\mathbf K_n$ of regular pseudocomplemented de Morgan and Kleene algebras of range $n$, respectively. Priestley duality as it applies to pseudocomplemented de Morgan algebras is used. We characterise the dual spaces of the simple (equivalently, subdirectly irreducible) algebras in $\mathbf M_n$ and explicitly describe the dual spaces of the simple algebras in $\mathbf M_1$ and $\mathbf K_1$. We show that the variety $\mathbf M_1$ is locally finite, but this property does not extend to $\mathbf M_n$ or even $\mathbf K_n$ for $n \geq 2$. We also show that the lattice of subvarieties of $\mathbf K_1$ is an $\omega + 1$ chain and the cardinality of the lattice of subvarieties of either $\mathbf K_2$ or $\mathbf M_1$ is $2^{\omega}$. A description of the lattice of subvarieties of $\mathbf M_1$ is given. Comment: 29 pages; 2 figures |
| Databáze: | OpenAIRE |
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