Ideals as generalized prime ideal factorization of submodules
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917067666489344 |
|---|---|
| author | Thulasi, K. R. Duraivel, T. Mangayarcarassy, S. |
| author_facet | Thulasi, K. R. Duraivel, T. Mangayarcarassy, S. |
| contents | For a submodule $N$ of an $R$-module $M$, a unique product of prime ideals in $R$ is assigned, which is called the generalized prime ideal factorization of $N$ in $M$, and denoted as ${\mathcal{P}}_M(N)$. But for a product of prime ideals ${{\mathfrak{p}_1} \cdots {\mathfrak{p}_{n}}}$ in $R$ and an $R$-module $M$, there may not exist a submodule $N$ in $M$ with ${\mathcal{P}}_{M}(N) = {{\mathfrak{p}_1} \cdots {\mathfrak{p}_{n}}}$. In this article, for an arbitrary product of prime ideals ${{\mathfrak{p}_1} \cdots {\mathfrak{p}_{n}}}$ and a module $M$, we find conditions for the existence of submodules in $M$ having ${{\mathfrak{p}_1} \cdots {\mathfrak{p}_{n}}}$ as their generalized prime ideal factorization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01573 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ideals as generalized prime ideal factorization of submodules Thulasi, K. R. Duraivel, T. Mangayarcarassy, S. Commutative Algebra Primary: 13A05, Secondary: 13A15, 13E05, 13E15 For a submodule $N$ of an $R$-module $M$, a unique product of prime ideals in $R$ is assigned, which is called the generalized prime ideal factorization of $N$ in $M$, and denoted as ${\mathcal{P}}_M(N)$. But for a product of prime ideals ${{\mathfrak{p}_1} \cdots {\mathfrak{p}_{n}}}$ in $R$ and an $R$-module $M$, there may not exist a submodule $N$ in $M$ with ${\mathcal{P}}_{M}(N) = {{\mathfrak{p}_1} \cdots {\mathfrak{p}_{n}}}$. In this article, for an arbitrary product of prime ideals ${{\mathfrak{p}_1} \cdots {\mathfrak{p}_{n}}}$ and a module $M$, we find conditions for the existence of submodules in $M$ having ${{\mathfrak{p}_1} \cdots {\mathfrak{p}_{n}}}$ as their generalized prime ideal factorization. |
| title | Ideals as generalized prime ideal factorization of submodules |
| topic | Commutative Algebra Primary: 13A05, Secondary: 13A15, 13E05, 13E15 |
| url | https://arxiv.org/abs/2309.01573 |