Rings with 2-$Δ$U property
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915095532011520 |
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| author | Hasanzadeh, Omid Moussavi, Ahmad Danchev, Peter |
| author_facet | Hasanzadeh, Omid Moussavi, Ahmad Danchev, Peter |
| contents | Rings in which the square of each unit lies in $1+Δ(R)$, are said to be $2$-$ΔU$, where $J(R)\subseteqΔ(R) =: \{r \in R | r + U(R) \subseteq U(R)\}$. The set $Δ(R)$ is the largest Jacobson radical subring of $R$ which is closed with respect to multiplication by units of $R$ and is studied in \cite{2}. The class of $2$-$ΔU$ rings consists several rings including $UJ$-rings, $2$-$UJ$ rings and $ΔU$-rings, and we observe that $ΔU$-rings are $UUC$. The structure of $2$-$ΔU$ rings is studied under various conditions. Moreover, the $2$-$ΔU$ property is studied under some algebraic constructions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04720 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rings with 2-$Δ$U property Hasanzadeh, Omid Moussavi, Ahmad Danchev, Peter Rings and Algebras Representation Theory 16S34, 16U60 Rings in which the square of each unit lies in $1+Δ(R)$, are said to be $2$-$ΔU$, where $J(R)\subseteqΔ(R) =: \{r \in R | r + U(R) \subseteq U(R)\}$. The set $Δ(R)$ is the largest Jacobson radical subring of $R$ which is closed with respect to multiplication by units of $R$ and is studied in \cite{2}. The class of $2$-$ΔU$ rings consists several rings including $UJ$-rings, $2$-$UJ$ rings and $ΔU$-rings, and we observe that $ΔU$-rings are $UUC$. The structure of $2$-$ΔU$ rings is studied under various conditions. Moreover, the $2$-$ΔU$ property is studied under some algebraic constructions. |
| title | Rings with 2-$Δ$U property |
| topic | Rings and Algebras Representation Theory 16S34, 16U60 |
| url | https://arxiv.org/abs/2501.04720 |