Article
| Title: | $(d,\frak b)$-injectivity and some ideal transforms (English) |
| Author: | Ghaffari, Ahad |
| Author: | Zamani, Naser |
| Author: | Sayedsadeghi, Mirsadegh |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 1 |
| Year: | 2026 |
| Pages: | 87-103 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ be a commutative ring with identity and $M$ be an $R$-module. For a nonnegative integer $d$ and an ideal $\frak b$ of $R$, the concept of $(d,\frak b)$-injectivity in the category of $R$-modules is defined. We characterize the $(d,\frak b)$-injective hull of a module $M$ as a submodule of $E(M)$. Then we focus on the case when the ring $R$ is Noetherian and see the connection with some modules caused by some ideal transform functor $T_{(d,\frak b)}(-)$ and some local cohomology functors $H^i_{(d,\frak b)}(-)$ based on $(d,\frak b)$. As results we will see that over a Noetherian ring the functors $\Gamma _{(d,\frak b)}(-)$ and $T_{(d,\frak b)}(-)$ preserve the ${(d,\frak b)}$-injectivity. Among other results, for a $(d,\frak b)$-torsion free module $M$, we find a condition under which $T_{(d,\frak b)}(M)$ is injective. (English) |
| Keyword: | injective module |
| Keyword: | torsion submodule |
| Keyword: | local cohomology |
| Keyword: | $d$-transform |
| MSC: | 13C05 |
| MSC: | 13C12 |
| MSC: | 13D45 |
| MSC: | 16D70 |
| DOI: | 10.21136/CMJ.2026.0119-25 |
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| Date available: | 2026-03-13T09:29:19Z |
| Last updated: | 2026-03-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153562 |
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