{
  "id": "1606.04059",
  "version": "v1",
  "published": "2016-06-13T18:23:12.000Z",
  "updated": "2016-06-13T18:23:12.000Z",
  "title": "Reducibility versus definability for pseudovarieties of semigroups",
  "authors": [
    "J. Almeida",
    "O. Klíma"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "It is easy to show that a pseudovariety which is reducible with respect to an implicit signature $\\sigma$ for the equation $x=y$ can also be defined by $\\sigma$-identities. We present several negative examples for the converse using signatures in which the pseudovarieties are usually defined. An ordered example issue from the extended Straubing-Th\\'erien hierarchy of regular languages is also shown to provide a positive example for the inequality $x\\le y$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-13T18:23:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M07"
    ],
    "keywords": [
      "pseudovariety",
      "reducibility",
      "semigroups",
      "definability",
      "implicit signature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}