{
  "id": "2103.11679",
  "version": "v1",
  "published": "2021-03-22T09:18:10.000Z",
  "updated": "2021-03-22T09:18:10.000Z",
  "title": "$δ$-$n$-ideals of commutative rings",
  "authors": [
    "Ece Yetkin Celikel",
    "Gulsen Ulucak"
  ],
  "categories": [
    "math.AC"
  ],
  "abstract": "Let $R$ be a commutative ring with nonzero identity, and $\\delta :\\mathcal{I(R)}\\rightarrow\\mathcal{I(R)}$ be an ideal expansion where $\\mathcal{I(R)}$ the set of all ideals of $R$. In this paper, we introduce the concept of $\\delta$-$n$-ideals which is an extension of $n$-ideals in commutative rings. We call a proper ideal $I$ of $R$ a $\\delta$-$n$-ideal if whenever $a,b\\in R$ with$\\ ab\\in I$ and $a\\notin\\sqrt{0}$, then $b\\in \\delta(I)$. For example, $\\delta_{1}$ is defined by $\\delta_{1}(I)=\\sqrt{I}.$ A number of results and characterizations related to $\\delta$-$n$-ideals are given. Furthermore, we present some results related to quasi $n$-ideals which is for the particular case $\\delta=\\delta_{1}.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-22T09:18:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "commutative ring",
      "nonzero identity",
      "ideal expansion",
      "proper ideal",
      "characterizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}