Rings in which all elements are the sum of a central element and an element from $Δ(R)$
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909525606400000 |
|---|---|
| author | Danchev, Peter Javan, Arash Hasanzadeh, Omid Moussavi, Ahmad |
| author_facet | Danchev, Peter Javan, Arash Hasanzadeh, Omid Moussavi, Ahmad |
| contents | We define and consider in-depth the so-called $CΔ$ rings as those rings $R$ whose elements are a sum of an element in $C(R)$ and of an element in $Δ(R)$. Our achieved results somewhat strengthen these recently obtained by Ma-Wang-Leroy in Czechoslovak Math. J. (2024) as well as these due to Kurtulmaz-Halicioglu-Harmanci-Chen in Bull. Belg. Math. Soc. Simon Stevin (2019).
Specifically, we succeeded to establish that exchange $CΔ$ rings are always clean as well as that exchange CN rings are strongly clean. Likewise, we prove that, for any ring $R$, the ring of formal power series $R[[x]]$ over $R$ is $CΔ$ if, and only if, so is $R$. And, furthermore, we show that, for any ring $R$, if the polynomial ring $R[x]$ is a $CΔ$ ring, then $R$ satisfies the Köthe conjecture. Some other closely related things concerning certain extensions of $CΔ$ rings are also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rings in which all elements are the sum of a central element and an element from $Δ(R)$ Danchev, Peter Javan, Arash Hasanzadeh, Omid Moussavi, Ahmad Rings and Algebras Representation Theory 16 S34, 16 U60 We define and consider in-depth the so-called $CΔ$ rings as those rings $R$ whose elements are a sum of an element in $C(R)$ and of an element in $Δ(R)$. Our achieved results somewhat strengthen these recently obtained by Ma-Wang-Leroy in Czechoslovak Math. J. (2024) as well as these due to Kurtulmaz-Halicioglu-Harmanci-Chen in Bull. Belg. Math. Soc. Simon Stevin (2019). Specifically, we succeeded to establish that exchange $CΔ$ rings are always clean as well as that exchange CN rings are strongly clean. Likewise, we prove that, for any ring $R$, the ring of formal power series $R[[x]]$ over $R$ is $CΔ$ if, and only if, so is $R$. And, furthermore, we show that, for any ring $R$, if the polynomial ring $R[x]$ is a $CΔ$ ring, then $R$ satisfies the Köthe conjecture. Some other closely related things concerning certain extensions of $CΔ$ rings are also presented. |
| title | Rings in which all elements are the sum of a central element and an element from $Δ(R)$ |
| topic | Rings and Algebras Representation Theory 16 S34, 16 U60 |
| url | https://arxiv.org/abs/2503.03643 |