{
  "id": "2005.12983",
  "version": "v1",
  "published": "2020-05-26T19:06:18.000Z",
  "updated": "2020-05-26T19:06:18.000Z",
  "title": "On $φ$-1-Absorbing Prime Ideals",
  "authors": [
    "Eda Yıldız",
    "Ünsal Tekir",
    "Suat Koç"
  ],
  "comment": "10 pages. arXiv admin note: text overlap with arXiv:2005.10365",
  "categories": [
    "math.AC"
  ],
  "abstract": "In this paper, we introduce $\\phi$-1-absorbing prime ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity $1\\neq0$ and $\\phi:\\mathcal{I}(R)\\rightarrow\\mathcal{I}(R)\\cup\\{\\emptyset\\}$ be a function where $\\mathcal{I}(R)$ is the set of all ideals of $R$. A proper ideal $I$ of $R$ is called a $\\phi$-1-absorbing prime ideal if for each nonunits $x,y,z\\in R$ with $xyz\\in I-\\phi(I)$, then either $xy\\in I$ or $z\\in I$. In addition to give many properties and characterizations of $\\phi$-1-absorbing prime ideals, we also determine rings in which every proper ideal is $\\phi$-1-absorbing prime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-26T19:06:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A15",
      "13C05",
      "54C35"
    ],
    "keywords": [
      "prime ideal",
      "proper ideal",
      "determine rings",
      "nonzero identity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}