{
  "id": "2001.06134",
  "version": "v1",
  "published": "2020-01-17T01:49:37.000Z",
  "updated": "2020-01-17T01:49:37.000Z",
  "title": "Varieties of Regular Pseudocomplemented de Morgan Algebras",
  "authors": [
    "M. E. Adams",
    "H. P. Sankappanavar",
    "Júlia Vaz de Carvalho"
  ],
  "comment": "29 pages; 2 figures",
  "doi": "10.1007/s11083-019-09518-y",
  "categories": [
    "math.LO"
  ],
  "abstract": "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 $\\omega + 1$ chain and the cardinality of the lattice of subvarieties of either $\\mathbf K_2$ or $\\mathbf M_1$ is $2^{\\omega}$. A description of the lattice of subvarieties of $\\mathbf M_1$ is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-17T01:49:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06D30",
      "06D15",
      "03G25",
      "08B15",
      "06D50",
      "03G10"
    ],
    "keywords": [
      "morgan algebras",
      "dual spaces",
      "subvarieties",
      "simple algebras",
      "priestley duality"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}