Article
| Title: | On quasi $n$-ideals of commutative rings (English) |
| Author: | Anebri, Adam |
| Author: | Mahdou, Najib |
| Author: | Aslankarayiğit Uğurlu, Emel |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 4 |
| Year: | 2022 |
| Pages: | 1133-1144 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | $n$-ideal |
| Keyword: | quasi $n$-ideal |
| Keyword: | $(2,n)$-ideal |
| MSC: | 13A15 |
| MSC: | 13A18 |
| idZBL: | Zbl 07655788 |
| idMR: | MR4517601 |
| DOI: | 10.21136/CMJ.2022.0365-21 |
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| Date available: | 2022-11-28T11:40:26Z |
| Last updated: | 2023-04-11 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151135 |
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