{
  "id": "1503.05075",
  "version": "v1",
  "published": "2015-03-17T14:38:12.000Z",
  "updated": "2015-03-17T14:38:12.000Z",
  "title": "Characterization of Pomonoids by Properties of Generators",
  "authors": [
    "Setareh Irannezhad",
    "Ali Madanshekaf"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "The study of flatness properties of ordered monoids acting on posets was initiated by S.M. Fakhruddin in the 1980's. Although there exist many papers which investigate various properties of $S$-posets (posets equipped with a compatible right action of an ordered monoid $S$) from free to torsion free, among them generators, there seems to be known very little. In 2008, Laan characterized generators in the category {\\bf Pos}-$S$ of all $S$-posets with monotone action-preserving maps between them. His characterization is similar to the case of acts over monoids. We attempt here to collect the knowledge on generators in the category {\\bf Pos}-$S$ and to apply this to proceed on the questions of homological classification of ordered monoids, that is results of the type: all generators in the category {\\bf Pos}-$S$, satisfy a flatness property if and only if $S$ has a certain property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-17T14:38:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M50",
      "06F05"
    ],
    "keywords": [
      "characterization",
      "ordered monoid",
      "flatness property",
      "monotone action-preserving maps",
      "compatible right action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}