Czechoslovak Mathematical Journal, Vol. 72, No. 4, pp. 1133-1144, 2022
On quasi $n$-ideals of commutative rings
Adam Anebri, Najib Mahdou, Emel Aslankarayiğit Uğurlu
Received September 29, 2021. Published online July 28, 2022.
Abstract: 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 $(2,n)$-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 $pr$-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.
Keywords: $n$-ideal; quasi $n$-ideal; $(2,n)$-ideal
Affiliations: Adam Anebri, Najib Mahdou, Laboratory of Modelling and Mathematical Structures, Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S.M. Ben Abdellah Fez, Morocco, e-mail: adam.anebri@usmba.ac.ma, mahdou@hotmail.com, Emel Aslankarayiğit Uğurlu (corresponding author), Department of Mathematics, Marmara University, Istanbul, Turkey, e-mail: emelakyugurlu@gmail.com
