Article
| Title: | $(m,n)$-prime ideals of commutative rings (English) |
| Author: | Khashan, Hani A. |
| Author: | Yetkin Çelikel, Ece |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 3 |
| Year: | 2025 |
| Pages: | 1073-1091 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ be a commutative ring with identity and $m$, $n$ be positive integers. We introduce the class of $(m,n)$-prime ideals which lies properly between the classes of prime and $(m,n)$-closed ideals. A proper ideal $I$ of $R$ is called $(m,n)$-prime if for $a,b\in R$, $a^{m}b\in I$ implies either $a^{n}\in I$ or $b\in I.$ Several characterizations of this new class with many examples are given. Analogous to primary decomposition, we define the \hbox {$(m,n)$-decomposition} of ideals and show that every ideal in an $n$-Noetherian ring has an $(m,n)$-decomposition. Furthermore, the $(m,n)$-prime avoidance theorem is proved. (English) |
| Keyword: | $(m,n)$-prime ideal |
| Keyword: | $(m,n)$-closed ideal |
| Keyword: | $n$-absorbing ideal |
| Keyword: | avoidance theorem |
| MSC: | 13A15 |
| MSC: | 13F05 |
| DOI: | 10.21136/CMJ.2025.0090-25 |
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| Date available: | 2025-09-19T12:11:16Z |
| Last updated: | 2025-09-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153067 |
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