On quasi $n$-ideals of commutative rings

Anebri, Adam, Mahdou, Najib, and Aslankarayiğit Uğurlu, Emel. "On quasi $n$-ideals of commutative rings." Czechoslovak Mathematical Journal 72.4 (2022): 1133-1144. <http://eudml.org/doc/298937>.

@article{Anebri2022,
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.},
author = {Anebri, Adam, Mahdou, Najib, Aslankarayiğit Uğurlu, Emel},
journal = {Czechoslovak Mathematical Journal},
keywords = {$n$-ideal; quasi $n$-ideal; $(2,n)$-ideal},
language = {eng},
number = {4},
pages = {1133-1144},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On quasi $n$-ideals of commutative rings},
url = {http://eudml.org/doc/298937},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Anebri, Adam
AU - Mahdou, Najib
AU - Aslankarayiğit Uğurlu, Emel
TI - On quasi $n$-ideals of commutative rings
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 4
SP - 1133
EP - 1144
AB - 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.
LA - eng
KW - $n$-ideal; quasi $n$-ideal; $(2,n)$-ideal
UR - http://eudml.org/doc/298937
ER -