伪补Kleene代数的子簇
Subvarieties of Pseudocomplemented Kleene Algebras
摘要：
本文利用伪补De Morgan代数簇${\cal PCDM}$的De Morgan $p$ -空间研究了伪补De Morgan代数簇中的次直不可约代数。引入了代数${\bf L} \in {\cal PCDM}$的$body$的概念，当${\bf L}$是次直不可约的时，确定了$Body({\bf L})$.因此，在伪补Kleene代数的情况下，三个特殊的子簇自然产生，我们给出明确的身份，他们的特点。我们还引入了${\cal PCDM}$的一个子簇${\cal BPK}$，即$bundle$ $pseudocomplemented$ $Kleene$ $algebras$的簇，确定了整个子簇格，并为每个子簇找到了显式的方程基.此外，我们还研究了由${\cal BPK}$的单成员生成的${\cal BPK}$的子簇${\cal BPK}_0$，确定了有限集上自由代数及其有限弱投射代数的结构.
英文摘要：
In this paper we study the subdirectly irreducible algebras in the variety ${\cal PCDM}$ of pseudocomplemented De Morgan algebras by means of their De Morgan $p$-spaces. We introduce the notion of $body$ of an algebra ${\bf L} \in {\cal PCDM}$ and determine $Body({\bf L})$ when ${\bf L}$ is subdirectly irreducible. As a consequence of this, in the case of pseudocomplemented Kleene algebras, three special subvarieties arise naturally, for which we give explicit identities that characterize them. We also introduce a subvariety ${\cal BPK}$ of ${\cal PCDM}$, namely the variety of $bundle$ $pseudocomplemented$ $Kleene$ $algebras$, determine the whole subvariety lattice and find explicit equational bases for each of the subvarieties. In addition, we study the subvariety ${\cal BPK}_0$ of ${\cal BPK}$ generated by the simple members of ${\cal BPK}$, determine the structure of the free algebra over a finite set and their finite weakly projective algebras.
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