Article
| Title: | Weakly $S$-$J$-ideal (English) |
| Author: | Smach, Sihem |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 2 |
| Year: | 2026 |
| Pages: | 635-643 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ be a commutative ring with identity. The notion of $S$-$J$-ideal was introduced in U. Tekir, S. Koc, and K. H. Oral (2017) as a generalization of $J$-ideal. We introduce a weaker version of $J$-ideals by defining the concept of weakly $S$-$J$-ideal. Let $S\subseteq \nobreak R$ be a multiplicatively closed subset of $R$. A proper ideal $I$ of $R$ disjoint with $S$ is called a weakly $S$-$J$-ideal of $R$ if whenever $ab\in I$ for $a,b\in R$, then there exists $s\in S$ such that $sa\in \mathcal {J}(R)$ or $sb\in I$. We investigate many properties and characterizations of weakly $S$-$J$-ideals. (English) |
| Keyword: | $n$-ideal |
| Keyword: | $J$-ideal |
| Keyword: | commutative ring |
| Keyword: | multiplicatively closed subset |
| Keyword: | weakly $S$-$J$-ideal |
| MSC: | 13A15 |
| MSC: | 13A99 |
| MSC: | 13B30 |
| MSC: | 16N20 |
| DOI: | 10.21136/CMJ.2026.0387-25 |
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| Date available: | 2026-05-22T11:23:50Z |
| Last updated: | 2026-05-25 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153653 |
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| Reference: | [6] Farshad, N., Safarisabet, S. A., Moussavi, A.: Amalgamated rings with clean-type properties.Hacet. J. Math. Stat. 50 (2021), 1358-1370. Zbl 1499.16067, MR 4331405, 10.15672/hujms.676342 |
| Reference: | [7] Khashan, H. A., Bani-Ata, A. B.: $J$-ideals of commutative rings.Int. Electron. J. Algebra 29 (2021), 148-164. Zbl 1467.13005, MR 4206318, 10.24330/ieja.852139 |
| Reference: | [8] Mohamadian, R.: $r$-ideals in commutative rings.Turk. J. Math. 39 (2015), 733-749. Zbl 1348.13003, MR 3395802, 10.3906/mat-1503-35 |
| Reference: | [9] Nagata, M.: Local Rings.Interscience Tracts in Pure and Applied Mathematics 13. John Wiley & Sons, New York (1962). Zbl 0123.03402, MR 0155856 |
| Reference: | [10] Tekir, U., Koc, S., Oral, K. H.: $n$-ideals of commutative rings.Filomat 31 (2017), 2933-2941. Zbl 1488.13016, MR 3639382, 10.2298/FIL1710933T |
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