Article
| Title: | On $S$-$(\delta , 2)$-primary ideals of a commutative ring (English) |
| Author: | Bakkari, Chahrazade |
| Author: | Hachache, Rachid |
| Author: | Koç, Suat |
| Author: | Mahdou, Najib |
| Author: | Tekir, Ünsal |
| Author: | Leoreanu-Fotea, Violeta |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 1 |
| Year: | 2026 |
| Pages: | 287-302 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ be a commutative ring with identity, $S$ be a multiplicative set of $R$, ${\rm Id}(R)$ be the set of all ideals of $R$, and $\delta \colon {\rm Id}(R) \rightarrow {\rm Id}(R)$ be a function. Then $\delta $ is called an expansion function of ideals of $R$ if whenever $L$, $I$, $J$ are ideals of $R$ with $J \subseteq I$, we have $L \subseteq \delta (L)$ and $\delta (J)\subseteq \delta (I)$. Let $\delta $ be an expansion function of ideals of $R$. We introduce the concept of $S$-$(\delta , 2)$-primary ideal which is a generalization of $(\delta ,2)$-primary ideal. Let $P$ be a proper ideal of $R$ disjoint with $S$. We say that $P$ is an $S$-$(\delta , 2)$-primary ideal of $R$ if there exists $s \in S$ such that for all $a,b \in R$, if $ab \in P$, then $sa^2 \in P$ or $sb^2 \in \delta (P)$. We next study the possible transfer of the above ideal property to the direct product of rings, quotient rings, localizations, trivial ring extensions, and amalgamation rings along an ideal. (English) |
| Keyword: | $S$-$(\delta , 2)$-primary ideal |
| Keyword: | $S$-2-prime ideal |
| Keyword: | idealization |
| Keyword: | amalgamated algebra |
| MSC: | 13A15 |
| MSC: | 13B25 |
| MSC: | 13C05 |
| DOI: | 10.21136/CMJ.2026.0349-25 |
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| Date available: | 2026-03-13T09:34:24Z |
| Last updated: | 2026-03-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153573 |
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