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arXiv · 2102.07823

Weakly J-ideals of Commutative Rings

Hani A. Khashan·Ece Yetkin Celikel
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Abstract

Let $R$ be a commutative ring with non-zero identity. In this paper, we introduce the concept of weakly $J$-ideals as a new generalization of $J$-ideals. We call a proper ideal $I$ of a ring $R$ a weakly $J$-ideal if whenever $a,b\in R$ with $0\neq ab\in I$ and $a\notin J(R)$, then $a\in I$. Many of the basic properties and characterizations of this concept are studied. We investigate weakly $J$-ideals under various contexts of constructions such as direct products, localizations, homomorphic images. Moreover, a number of examples and results on weakly $J$-ideals are discussed. Finally, the third section is devoted to the characterizations of these constructions in an amagamated ring along an ideal.

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Hani A. Khashan, Ece Yetkin Celikel. 2021-02-15. Weakly J-ideals of Commutative Rings. https://arxiv.org/abs/2102.07823

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