{
  "id": "1312.5589",
  "version": "v2",
  "published": "2013-12-19T15:31:50.000Z",
  "updated": "2015-05-05T15:35:01.000Z",
  "title": "On free products and amalgams of pomonoids",
  "authors": [
    "Bana Al Subaiei",
    "James Renshaw"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "The study of amalgamation in the category of partially ordered monoids was initiated by Fakhuruddin in the 1980s. In 1986 he proved that, in the category of commutative pomonoids, every absolutely flat commutative pomonoid is a weak amalgmation base and every commutative pogroup is a strong amalgamation base. Some twenty years later, Bulman-Fleming and Sohail in 2011 extended this work to what they referred to as pomonoid amalgams. In particular they proved that pogroups are poamalgmation bases in the category of pomonoids. Sohail, also in 2011, proved that absolutely poflat commutative pomonoids are poamalgmation bases in the category of commutative pomonoids. In the present paper we extend the work on pomonoid amalgams by generalising the work of Renshaw on amalgams of monoids and extension properties of acts over monoids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-19T15:31:50.000Z",
      "abstract": "The study of amalgamation in the category of partially ordered monoids was initiated by Fakhuruddin in the 1980s. In [5] he proved that an absolutely flat commutative pomonoid is a weak amalgmation base in the category of commutative pomonoids. He also proved that every commutative pogroup is a strong amalgmation base in the category of commutative pomonoids. After more that twenty years, Bulman-Fleming and Sohail in 2011 extended this work to what they referred to as pomonoid amalgams, and details of their work can be found in [3] and [4]. In particular they proved that pogroups are poamalgmation bases in the category of pomonoids. Sohail in [10] proved that absolutely poflat commutative pomonoids are poamalgmation bases in the category of commutative pomonoids. In this paper we extend the work on pomonoid amalgams by generalising the work of Renshaw [11] on amalgams of monoids and extension properties of acts over monoids.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-05-05T15:35:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M30",
      "06F05"
    ],
    "keywords": [
      "free products",
      "pomonoid amalgams",
      "poamalgmation bases",
      "weak amalgmation base",
      "strong amalgamation base"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.5589S"
    }
  }
}