Rings such that, for each unit $u$, $u^n-1$ belongs to the $Δ(R)$

We study in-depth those rings $R$ for which, there exists a fixed $n \geq 1$ , such that $u^{n} - 1$ lies in the subring $Δ (R)$ of $R$ for every unit $u \in R$ . We succeeded to describe for any $n \geq 1$ all reduced $π$ -regular $(2 n - 1)$ - $Δ$ U rings by showing that they satisfy the equation $x^{2 n} = x$ as well as to prove that the property of being exchange and clean are tantamount in the class of $(2 n - 1)$ - $Δ$ U rings. These achievements considerably extend results established by Danchev (Rend. Sem. Mat. Univ. Pol. Torino, 2019) and Koşan et al. (Hacettepe J. Math. & Stat., 2020). Some other closely related results of this branch are also established.

Rings such that, for each unit $u$ , $u^{n} - 1$ belongs to the $Δ (R)$

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Rings such that, for each unit $u$ , $u^{n} - 1$ belongs to the $Δ (R)$

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Rings such that, for each unit uu, un−1un−1 belongs to the Δ(R)Δ(R)

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Rings such that, for each unit uu, un−1un−1 belongs to the Δ(R)Δ(R)

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Rings such that, for each unit $u$ , $u^{n} - 1$ belongs to the $Δ (R)$

讲解博客

AI智能校验

Rings such that, for each unit $u$ , $u^{n} - 1$ belongs to the $Δ (R)$

讲解博客

AI智能校验