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Varieties of Regular Pseudocomplemented de Morgan Algebras
Order ( IF 0.6 ) Pub Date : 2020-01-10 , DOI: 10.1007/s11083-019-09518-y
M. E. Adams , H. P. Sankappanavar , Júlia Vaz de Carvalho

In this paper, we investigate the varieties M n and 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 M n and explicitly describe the dual spaces of the simple algebras in M 1 and K 1 . We show that the variety M 1 is locally finite, but this property does not extend to M n or even K n for n =?2. We also show that the lattice of subvarieties of K 1 is an ? +?1 chain and the cardinality of the lattice of subvarieties of either K 2 or M 1 is 2 ? . A description of the lattice of subvarieties of M 1 is given.

中文翻译:

各种正则伪互补 de Morgan 代数

在本文中,我们分别研究了范围为 n 的正则赝补 de Morgan 和 Kleene 代数的变体 M n 和 K n 。使用 Priestley 对偶性,因为它适用于伪补 de Morgan 代数。我们刻画了 M n 中简单(等价地,次直接不可约)代数的对偶空间,并明确描述了 M 1 和 K 1 中简单代数的对偶空间。我们证明了多样性 M 1 是局部有限的,但是对于 n =?2,这个性质不能扩展到 M n 甚至 K n 。我们还证明了 K 1 的子变体的格是一个 ? +?1 链和 K 2 或 M 1 的子变体的格的基数是 2 ? . 给出了M 1 的子变体的格子的描述。
更新日期:2020-01-10
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