Article
| Title: | On weakly $(1,n)$-ideals and weakly $n$-ideals (English) |
| Author: | Ersoy, Bayram Ali |
| Author: | Koç, Suat |
| Author: | Tekir, Ünsal |
| Author: | Yeşilot, Gürsel |
| Author: | Yıldız, Eda |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 2 |
| Year: | 2025 |
| Pages: | 611-628 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study weakly $(1,n)$-ideals and weakly $n$-ideals in commutative rings. Let $A$ be a commutative ring with a nonzero identity and $I$ be a proper ideal of $A$. Then $I$ is said to be a weakly $(1,n)$-ideal (or weakly $n$-ideal) if whenever $0\neq abc\in I$ for some nonunits $a,b,c\in A$ (or $0\neq ab\in I$ for some $a,b\in A)$, then either $ab\in I$ or $c\in \mathfrak {N}(A)$ (or $a\in I$ or $b\in \mathfrak {N}(A)$, respectively), where $\mathfrak {N}(A)$ is the set of all nilpotent elements of $A$. Many examples and properties of weakly $(1,n)$-ideals and weakly $n$-ideals are given. We characterize all rings in which every proper ideal is a weakly $(1,n)$-ideal and weakly $n$-ideal. Furthermore, we investigate both weakly $(1,n)$-ideals and weakly $n$-ideals in amalgamated algebras along an ideal. (English) |
| Keyword: | 1-absorbing primary ideal |
| Keyword: | $n$-ideal |
| Keyword: | weakly $n$-ideal |
| Keyword: | weakly $(1,n)$-ideal |
| MSC: | 13A15 |
| DOI: | 10.21136/CMJ.2025.0337-24 |
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| Date available: | 2025-05-20T11:48:45Z |
| Last updated: | 2025-05-26 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152961 |
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