{
  "id": "2005.10365",
  "version": "v1",
  "published": "2020-05-20T21:39:16.000Z",
  "updated": "2020-05-20T21:39:16.000Z",
  "title": "On Weakly 1-Absorbing Prime Ideals",
  "authors": [
    "Suat Koç",
    "Ünsal Tekir",
    "Eda Yıldız"
  ],
  "comment": "14 pages, original research paper",
  "categories": [
    "math.AC"
  ],
  "abstract": "This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let $A$ be a commutative ring with a nonzero identity $1\\neq 0$. A proper ideal $P$ of $A$ is said to be a weakly 1-absorbing prime ideal if for each nonunits $x, y, z \\in A$ with $0\\neq xyz \\in P$, then either $xy \\in P$ or $z \\in P$. In addition to give many properties and characterizations of weakly 1-absorbing prime ideals, we also determine rings in which every proper ideal is weakly 1-absorbing prime. Furthermore, we investigate weakly 1-absorbing prime ideals in $C(X)$, which is the ring of continuous functions of a topological space X.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-20T21:39:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A15",
      "13C05",
      "54C35"
    ],
    "keywords": [
      "prime ideal",
      "proper ideal",
      "nonzero identity",
      "determine rings",
      "commutative ring"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}