Geodesic
On quasi $n$-ideals of commutative rings
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 1133-1144.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{10_21136_CMJ_2022_0365_21,
     author = {Anebri, Adam and Mahdou, Najib and Aslankarayi\u{g}it U\u{g}urlu, Emel},
     title = {On quasi $n$-ideals of commutative rings},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1133--1144},
     publisher = {mathdoc},
     volume = {72},
     number = {4},
     year = {2022},
     doi = {10.21136/CMJ.2022.0365-21},
     mrnumber = {4517601},
     zbl = {07655788},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0365-21/}
}
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
SP  - 1133
EP  - 1144
VL  - 72
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0365-21/
DO  - 10.21136/CMJ.2022.0365-21
LA  - en
ID  - 10_21136_CMJ_2022_0365_21
ER  - 
%0 Journal Article
%A Anebri, Adam
%A Mahdou, Najib
%A Aslankarayiğit Uğurlu, Emel
%T On quasi $n$-ideals of commutative rings
%J Czechoslovak Mathematical Journal
%D 2022
%P 1133-1144
%V 72
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0365-21/
%R 10.21136/CMJ.2022.0365-21
%G en
%F 10_21136_CMJ_2022_0365_21
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. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0365-21/

Cité par Sources :