On the transfer of certain ring-theoretic properties in Anderson rings
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929554322358272 |
|---|---|
| author | Baek, Hyungtae Lim, Jung Wook Tamoussit, Ali |
| author_facet | Baek, Hyungtae Lim, Jung Wook Tamoussit, Ali |
| contents | Let $R$ be a commutative ring with unity and let $X$ be an indeterminate over $R$. The \textit{Anderson ring} of $R$ is defined as the quotient ring of the polynomial ring $R[X]$ by the set of polynomials that evaluate to $1$ at $0$. Specifically, the Anderson ring of $R$ is $R[X]_A$, where $A=\{f\in R[X]\mid f(0)=1\}$. In this paper, we aim to investigate the transfer of various ring-theoretic properties between the ring $R$ and its Anderson ring $R[X]_A$. Interesting results are established, accompanied by applications and illustrative examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the transfer of certain ring-theoretic properties in Anderson rings Baek, Hyungtae Lim, Jung Wook Tamoussit, Ali Commutative Algebra 13A15, 13B25, 13B30, 13F05 Let $R$ be a commutative ring with unity and let $X$ be an indeterminate over $R$. The \textit{Anderson ring} of $R$ is defined as the quotient ring of the polynomial ring $R[X]$ by the set of polynomials that evaluate to $1$ at $0$. Specifically, the Anderson ring of $R$ is $R[X]_A$, where $A=\{f\in R[X]\mid f(0)=1\}$. In this paper, we aim to investigate the transfer of various ring-theoretic properties between the ring $R$ and its Anderson ring $R[X]_A$. Interesting results are established, accompanied by applications and illustrative examples. |
| title | On the transfer of certain ring-theoretic properties in Anderson rings |
| topic | Commutative Algebra 13A15, 13B25, 13B30, 13F05 |
| url | https://arxiv.org/abs/2410.17007 |