Article
| Title: | $J$-prime ideals of commutative rings (English) |
| Author: | Assalami, Mohammed |
| Author: | Koç, Suat |
| Author: | Mahdou, Najib |
| Author: | Tekir, Ünsal |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 2 |
| Year: | 2026 |
| Pages: | 525-539 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ be a commutative ring with identity, and $J(R)$ denote the Jacobson radical of $R$. This paper introduces $J$-prime ideals, generalizing prime ideals, $n$-ideals, and $J$-ideals. A proper ideal $I$ of $R$ is a $J$-prime ideal if for every $a, b \in R$, $ab \in I$ implies $a\in I+J(R) $ or $b \in I$. We characterize rings in which every proper ideal is $J$-prime, showing that a ring has the property that every proper ideal is $J$-prime if and only if it is a quasi-local ring. Also, we show that (0) is a $J$-prime ideal if and only if the ring is présimplifiable. Furthermore, we examine $J$-prime ideal characteristics in various ring constructions, such as homomorphic image of rings, quotient rings, cartesian product rings, polynomial rings, power series rings, trivial ring extension and amalgamation rings. (English) |
| Keyword: | $J$-prime ideal |
| Keyword: | prime ideal |
| Keyword: | $J$-ideal |
| Keyword: | $n$-ideal |
| Keyword: | $r$-ideal |
| Keyword: | amalgamation |
| Keyword: | trivial ring extension |
| MSC: | 13A15 |
| MSC: | 13B25 |
| MSC: | 13C15 |
| MSC: | 13E99 |
| DOI: | 10.21136/CMJ.2026.0324-25 |
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| Date available: | 2026-05-22T11:21:16Z |
| Last updated: | 2026-05-25 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153647 |
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