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Keywords:
$n$-ideal; $J$-ideal; commutative ring; multiplicatively closed subset; weakly $S$-$J$-ideal
$n$-ideal; $J$-ideal; commutative ring; multiplicatively closed subset; weakly $S$-$J$-ideal
Summary:
Let $R$ be a commutative ring with identity. The notion of $S$-$J$-ideal was introduced in U. Tekir, S. Koc, and K. H. Oral (2017) as a generalization of $J$-ideal. We introduce a weaker version of $J$-ideals by defining the concept of weakly $S$-$J$-ideal. Let $S\subseteq \nobreak R$ be a multiplicatively closed subset of $R$. A proper ideal $I$ of $R$ disjoint with $S$ is called a weakly $S$-$J$-ideal of $R$ if whenever $ab\in I$ for $a,b\in R$, then there exists $s\in S$ such that $sa\in \mathcal {J}(R)$ or $sb\in I$. We investigate many properties and characterizations of weakly $S$-$J$-ideals.
References:
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