On a generalization of $r$-ideals in commutative rings

Mohamed Chhiti; Abdelhaq El Khalfi; Khalid Kaiba

doi:10.5269/bspm.68369

Mohamed Chhiti University Sidi Mohammed Ben Abdellah Fez, Morocco
Abdelhaq El Khalfi Faculty of Sciences Ain Chock, Hassan II University of Casablanca
Khalid Kaiba University Sidi Mohammed Ben Abdellah Fez

Abstract

Let $R$ be a commutative ring with nonzero identity, $J$ a proper ideal of $R$. In this paper, we present the concept of $H_J$-ideals in commutative rings. A proper ideal $I$ of R is called an $H_J$-ideal if whenever $a$, $b$ $\in R$ with $ab\in I$ and $(J:a) =J$ such that $(J:a)=\{x \in R : xa \in J\}$, then $b\in I$. Our purpose is to extend the concept of $r$-ideals to $H_J$-ideals of commutative rings. Then, we investigate the basic properties of $H_J$-ideals and also, we give some examples with regard to $H_J$-ideals.

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