$\delta$-$J$-ideals of commutative rings

Shuai Zeng; Weiwei Wang; Jiantao Li

$\delta$-$J$-ideals of commutative rings

Commutative Algebra 2021-04-21 v3

Authors: Shuai Zeng , Weiwei Wang , Jiantao Li

Abstract

Let $\mathcal{I}(R)$ be the set of all ideals of a ring $R$ , $\delta$ be an expansion function of $\mathcal{I}(R)$ . In this paper, the $\delta$ - $J$ -ideal of a commutative ring is defined, that is, if $a, b\in R$ and $ab\in I\in \mathcal{I}(R)$ , then $a\in J(R)$ (the Jacobson radical of $R$ ) or $b\in \delta(I)$ . Moreover, some properties of $\delta$ - $J$ -ideals are discussed,such as localizations, homomorphic images, idealization and so on.

Keywords

commutative rings delta-j-ideals expansion function jacobson radical localization idealization

Cite

@article{arxiv.2104.07187,
  title  = {$\delta$-$J$-ideals of commutative rings},
  author = {Shuai Zeng and Weiwei Wang and Jiantao Li},
  journal= {arXiv preprint arXiv:2104.07187},
  year   = {2021}
}

Comments

arXiv admin note: text overlap with arXiv:2103.11679. In the previous version, we made a mistake on the authors of a reference. We are sorry for this mistake and have corrected this typo

$\delta$-$J$-ideals of commutative rings

Abstract

Keywords

Cite

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