论文标题
伪安装的Kleene代数的亚地区
Subvarieties of Pseudocomplemented Kleene Algebras
论文作者
论文摘要
在本文中，我们通过其de Morgan $ p $ -spaces来研究假配置的de Morgan代数的品种$ {\ cal pcdm} $中的细分不可约代数。我们在{\ cal pcdm} $中介绍了代数$ {\ bf l} \的$ body $的概念，并确定$ {\ bf l} $时，当$ {\ bf l} $ subnirectly directirelirectly directly diredruce new。因此，就伪安装的kleene代数而言，自然出现了三个特殊的亚群，为此，我们给出了表征它们的明确身份。我们还引入了$ {\ cal pcdm} $的子各种$ {\ cal bpk} $，即$ bundle $ $ $ $ $ $ $ $ $ $ $ $ $ $ kleene $ $ elgebras $，确定整个子变量并找到整个子效率，并为每个亚varieties的expational equination base。此外，我们研究了由$ {\ cal bpk} $的简单成员生成的$ {\ cal bpk} $的子变量$ {\ cal bpk} _0 $ $ {\ cal bpk} $生成的，请确定有限套件的自由代数的结构，并确定其有限的弱项目代数。
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.
