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arXiv · 2402.15455

Rings with $u-1$ Quasinilpotent for Each Unit $u$

Peter Danchev·Arash Javan·Omid Hasanzadeh·Ahmad Moussavi
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Abstract

We define and explore in-depth the notion of {\it UQ rings} by showing their important properties and by comparing their behavior with that of the well-known classes of UU rings and JU rings, respectively. Specifically, among the other established results, we prove that UQ rings are always Dedekind finite (often named directly finite) as well as that, for semipotent rings $R$, the following equivalence hold: $R/J(R)$ is UQ $\iff$ $R$ is UQ having the property that the set $QN(R)$ of quasinilpotent elements of $R$ coincides with the Jacobson radical $J(R)$ of $R$.

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Peter Danchev, Arash Javan, Omid Hasanzadeh, Ahmad Moussavi. 2024-02-23. Rings with $u-1$ Quasinilpotent for Each Unit $u$. https://doi.org/10.1142/s0219498825502470

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