{
  "id": "1210.3285",
  "version": "v1",
  "published": "2012-10-11T16:14:51.000Z",
  "updated": "2012-10-11T16:14:51.000Z",
  "title": "A 2-base for inverse semigroups",
  "authors": [
    "Joao Araujo",
    "Michael Kinyon",
    "R. Padmanabhan"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "An open problem in the theory of inverse semigroups was whether the variety of such semigroups, when viewed as algebras with a binary operation and a unary operation, is 2-based, that is, has a base for its identities consisting of 2 independent axioms. In this note, we announce the affirmative solution to this problem: the identities \\[ \\quad x(x'x) = x \\qquad \\quad x (x' (y (y' ((z u)' w')'))) = y (y' (x (x' ((w z) u)))) \\] form a base for inverse semigroups where ${}'$ turns out to be the natural inverse operation. We recount here the history of the problem including our previous efforts to find a 2-base using automated deduction and the method that finally worked. We describe our efforts to simplify the proof using \\textsc{Prover9}, present the simplified proof itself and conclude with some open problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-11T16:14:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M18",
      "20M07"
    ],
    "keywords": [
      "inverse semigroups",
      "open problem",
      "natural inverse operation",
      "unary operation",
      "identities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.3285A"
    }
  }
}