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.
Categories: math.LO