Regular double p-algebras
| Autor: | Hanamantagouda P. Sankappanavar, M. E. Adams, Júlia Vaz de Carvalho |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Mathematica Slovaca. 69:15-34 |
| ISSN: | 1337-2211 0139-9918 |
| DOI: | 10.1515/ms-2017-0200 |
| Popis: | In this paper, we investigate the variety RDP of regular double p-algebras and its subvarieties RDP n , n ≥ 1, of range n. First, we present an explicit description of the subdirectly irreducible algebras (which coincide with the simple algebras) in the variety RDP 1 and show that this variety is locally finite. We also show that the lattice of subvarieties of RDP 1, LV (RDP 1), is isomorphic to the lattice of down sets of the poset {1} ⊕ (ℕ × ℕ). We describe all the subvarieties of RDP 1 and conclude that LV (RDP 1) is countably infinite. An equational basis for each proper subvariety of RDP 1 is given. To study the subvarieties RDP n with n ≥ 2, Priestley duality as it applies to regular double p-algebras is used. We show that each of these subvarieties is not locally finite. In fact, we prove that its 1-generated free algebra is infinite and that the lattice of its subvarieties has cardinality 2 ℵ 0 . We also use Priestley duality to prove that RDP and each of its subvarieties RDP n are generated by their finite members. |
| Databáze: | OpenAIRE |
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