Geodesic
On quasi $n$-ideals of commutative rings
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1133-1144
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Let $R$ be a commutative ring with a nonzero identity. In this study, we present a new class of ideals lying properly between the class of $n$-ideals and the class of \hbox {$(2,n)$-ideals}. A proper ideal $I$ of $R$ is said to be a quasi $n$-ideal if $\sqrt {I}$ is an $n$-ideal of $R.$ Many examples and results are given to disclose the relations between this new concept and others that already exist, namely, the $n$-ideals, the quasi primary ideals, the $(2,n)$-ideals and the \hbox {$pr$-ideals}. Moreover, we use the quasi $n$-ideals to characterize some kind of rings. Finally, we investigate quasi $n$-ideals under various contexts of constructions such as direct product, power series, idealization, and amalgamation of a ring along an ideal.
Let $R$ be a commutative ring with a nonzero identity. In this study, we present a new class of ideals lying properly between the class of $n$-ideals and the class of \hbox {$(2,n)$-ideals}. A proper ideal $I$ of $R$ is said to be a quasi $n$-ideal if $\sqrt {I}$ is an $n$-ideal of $R.$ Many examples and results are given to disclose the relations between this new concept and others that already exist, namely, the $n$-ideals, the quasi primary ideals, the $(2,n)$-ideals and the \hbox {$pr$-ideals}. Moreover, we use the quasi $n$-ideals to characterize some kind of rings. Finally, we investigate quasi $n$-ideals under various contexts of constructions such as direct product, power series, idealization, and amalgamation of a ring along an ideal.
DOI : 10.21136/CMJ.2022.0365-21
Classification : 13A15, 13A18
Keywords: $n$-ideal; quasi $n$-ideal; $(2, n)$-ideal 
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Anebri, Adam; Mahdou, Najib; Aslankarayiğit Uğurlu, Emel. On quasi $n$-ideals of commutative rings. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1133-1144. doi: 10.21136/CMJ.2022.0365-21

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