Article
| Title: | Weakly $S$-2-absorbing ideals (English) |
| Author: | Sihem, Smach |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 3 |
| Year: | 2025 |
| Pages: | 793-806 |
| 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 $S$-$2$-absorbing ideal was introduced by G. Ulucak, Ü. Tekir, S. Koç (2020) as a generalization of $2$-absorbing ideal. We introduce $a$ weaker version of 2-absorbing ideals by defining the concept of weakly-$S$-2-absorbing ideal. Let $S\subseteq R$ be a multiplicatively closed subset of $R$. A proper ideal $I$ of $R$ disjoint with $S$ is called a weakly $S$-2-absorbing ideal of $R$ if whenever $abc\in I$ for $a,b,c\in R$ then there exists $s\in S$ such that $sab\in I$ or $sbc\in I$ or $sac\in I$. We investigate many properties and characterizations of weakly $S$-2-absorbing ideals. (English) |
| Keyword: | $S$-2-absorbing ideal |
| Keyword: | weakly $S$-2-absorbing ideal |
| Keyword: | $S$-prime ideal |
| MSC: | 13A15 |
| MSC: | 13A99 |
| DOI: | 10.21136/CMJ.2025.0397-24 |
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| Date available: | 2025-09-19T11:47:33Z |
| Last updated: | 2025-09-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153052 |
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| Reference: | [2] Anderson, D. F., Badawi, A.: On $n$-absorbing ideals of commutative rings.Commun. Algebra 39 (2011), 1646-1672. Zbl 1232.13001, MR 2821499, 10.1080/00927871003738998 |
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| Reference: | [4] Badawi, A.: On 2-absorbing ideals of commutative rings.Bull. Aust. Math. Soc. 75 (2007), 417-429. Zbl 1120.13004, MR 2331019, 10.1017/S0004972700039344 |
| Reference: | [5] D'Anna, M., Finocchiaro, C. A., Fontana, M.: Properties of chains of prime ideals in an amalgamated algebra along an ideal.J. Pure Appl. Algebra 214 (2010), 1633-1641. Zbl 1191.13006, MR 2593689, 10.1016/j.jpaa.2009.12.008 |
| Reference: | [6] D'Anna, M., Fontana, M.: An amalgamated duplication of a ring along an ideal: The basic properties.J. Algebra Appl. 6 (2007), 443-459. Zbl 1126.13002, MR 2342602, 10.1142/S0219498807002326 |
| Reference: | [7] Hamed, A., Malek, A.: $S$-prime ideals of a commutative ring.Beitr. Algebra Geom. 61 (2020), 533-542. Zbl 1442.13010, MR 4127389, 10.1007/s13366-019-00476-5 |
| Reference: | [8] Nagata, M.: Local Rings.Interscience Tracts in Pure and Applied Mathematics 13. John Wiley & Sons, New York (1962). Zbl 0123.03402, MR 0155856 |
| Reference: | [9] Sihem, S., Sana, H.: On Anderson-Badawi conjectures.Beitr. Algebra Geom. 58 (2017), 775-785. Zbl 1390.13011, MR 3702976, 10.1007/s13366-017-0343-9 |
| Reference: | [10] Ulucak, G., Tekir, Ü., Koç, S.: On $S$-2-absorbing submodules and vn-regular modules.An. Ştiinţ. Univ. "Ovidius" Constanţa, Ser. Mat. 28 (2020), 239-257. Zbl 1488.13029, MR 4152440, 10.2478/auom-2020-0030 |
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