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arXiv · 2501.04720

Rings with 2-$\Delta$U property

Omid Hasanzadeh·Ahmad Moussavi·Peter Danchev
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Abstract

Rings in which the square of each unit lies in $1+\Delta(R)$, are said to be $2$-$\Delta U$, where $J(R)\subseteq\Delta(R) =: \{r \in R | r + U(R) \subseteq U(R)\}$. The set $\Delta (R)$ 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 $2$-$\Delta U$ rings consists several rings including $UJ$-rings, $2$-$UJ$ rings and $\Delta U$-rings, and we observe that $\Delta U$-rings are $UUC$. The structure of $2$-$\Delta U$ rings is studied under various conditions. Moreover, the $2$-$\Delta U$ property is studied under some algebraic constructions.

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Omid Hasanzadeh, Ahmad Moussavi, Peter Danchev. 2025-01-02. Rings with 2-$\Delta$U property. https://arxiv.org/abs/2501.04720

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