论文标题
常规伪安装的De Morgan代数的品种
Varieties of Regular Pseudocomplemented de Morgan Algebras
论文作者
论文摘要
在本文中，我们研究了常规伪安装的de Morgan和Kleene代数$ n $的品种$ \ MATHBF M_N $和$ \ MATHBF k_n $。 Priestley二元性适用于伪安装的De Morgan代数。我们在$ \ Mathbf m_n $中表征了简单（等效，细分不可约等）的双空间，并在$ \ mathbf m_1 $和$ \ \ \ \ mthbf k_1 $中明确描述简单代数的双空间。我们表明，品种$ \ Mathbf m_1 $是本地有限的，但是此属性不扩展到$ \ Mathbf m_n $，甚至$ \ Mathbf k_n $，for $ n \ geq 2 $。我们还表明，$ \ mathbf k_1 $的子视界晶格是$ω+ 1 $链，以及$ \ mathbf k_2 $或$ \ mathbf m_1 $ as subvarieties晶格的基数是$ 2^ω$。给出了$ \ mathbf m_1 $的子视线晶格的描述。
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 $ω+ 1$ chain and the cardinality of the lattice of subvarieties of either $\mathbf K_2$ or $\mathbf M_1$ is $2^ω$. A description of the lattice of subvarieties of $\mathbf M_1$ is given.
