In this paper we study the subdirectly irreducible algebras in the variety $\mathcal{PCD}\mathcal{M}$ of pseudocomplemented De Morgan algebras by means of their De Morgan p-spaces. We introduce the notion of the body of an algebra $\mathbf{L}\in \mathcal{PCD}\mathcal{M}$ and determine $\mathrm{Body}(\mathbf{L})$ when $\mathbf{L}$ is subdirectly irreducible. As a consequence of this, in the case of pseudocomplemented Kleene algebras, two special subvarieties arise naturally, for which we give explicit identities that characterise them. We also introduce a subvariety $\mathcal{BPK}$ of $\mathcal{PCD}\mathcal{M}$, namely the variety of bundle pseudocomplemented Kleene algebras, fully describe its subvariety lattice and find explicit equational bases for each subvariety. In addition, we study the subvariety ${\mathcal{BPK}}_0$ of $\mathcal{BPK}$ generated by the simple members of $\mathcal{BPK}$, determine the structure of the free algebra over a finite set in this variety and their finite weakly projective algebras.

中文翻译：

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拟补 Kleene 代数的种类

在本文中，我们研究了类中的次直接不可约代数 $\mathcal{PCD}\mathcal{米}$伪互补的德摩根代数通过他们的德摩根 p 空间。我们引入代数体的概念$\mathbf{升}\in \mathcal{PCD}\mathcal{米}$ 并确定 $\mathrm{身体}(\mathbf{升})$ 什么时候 $\mathbf{升}$是次直接不可约的。因此，在赝补 Kleene 代数的情况下，两个特殊的子变体自然出现，为此我们给出了表征它们的明确恒等式。我们还引入了一个子变体$\mathcal{BPK}$ 的 $\mathcal{PCD}\mathcal{米}$，即束赝补克林代数的变体，充分描述其子变体格并为每个子变体找到明确的方程基。此外，我们研究了子变体${\mathcal{BPK}}_0$ 的 $\mathcal{BPK}$ 由简单的成员生成 $\mathcal{BPK}$，确定自由代数在这个种类的有限集上的结构和它们的有限弱投影代数。