Article
| Title: | More on the strongly 1-absorbing primary ideals of commutative rings (English) |
| Author: | Yassine, Ali |
| Author: | Nikmehr, Mohammad Javad |
| Author: | Nikandish, Reza |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 1 |
| Year: | 2024 |
| Pages: | 115-126 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ be a commutative ring with identity. We study the concept of strongly \hbox {1-absorbing} primary ideals which is a generalization of $n$-ideals and a subclass of $1$-absorbing primary ideals. A proper ideal $I$ of $R$ is called strongly 1-absorbing primary if for all nonunit elements $a,b,c \in R$ such that $abc \in I$, it is either $ab \in I$ or $c \in \sqrt {0}$. Some properties of strongly 1-absorbing primary ideals are studied. Finally, rings $R$ over which every semi-primary ideal is strongly 1-absorbing primary, and rings $R$ over which every strongly \hbox {1-absorbing} primary ideal is prime (or primary) are characterized. Many examples are given to illustrate the obtained results. (English) |
| Keyword: | strongly 1-absorbing primary ideal |
| Keyword: | $n$-ideal |
| Keyword: | primary ideal |
| Keyword: | semi-primary ideal |
| MSC: | 13A15 |
| MSC: | 13C05 |
| DOI: | 10.21136/CMJ.2024.0525-22 |
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| Date available: | 2024-03-13T10:05:09Z |
| Last updated: | 2024-03-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152271 |
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