{
  "annotation_id": "1c48fe03-e298-4295-83e6-034ab63081b9",
  "date_created": "2026-02-17T05:53:16.019000Z",
  "date_modified": "2026-02-17T05:53:16.019000Z",
  "file_hash": "d95d487170c4a5cdf60929005ee1f4b617e1f9cc268c4fac2738246c45297686",
  "private": false,
  "record": {
    "abstract": "In this paper, we construct explicit families of transformation monoids whose augmentation submodules are simple and whose associated 0-minimal J-classes have rank greater than two. These examples provide new monoids with simple augmentation submodules and non-complete associated graphs. We also establish a connection between the sandwich matrix of a 0-minimal J-class of rank two and the simplicity of the corresponding augmentation module, yielding a criterion that determines simplicity directly from the rank of this matrix for this class of monoids.",
    "arxiv_id": "2601.08546",
    "authors": [
      "M. H. Shahzamanian"
    ],
    "categories": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Simplicity of Augmentation Submodules in Monoids with 0-Minimal Ideals of Rank Greater than Two",
    "url": "https://arxiv.org/abs/2601.08546",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b091f9b6-24f9-4eab-a093-c4dfccf8f17a",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}