Rings with Quasinilpotent for Each Unit
P Danchev, A Javan, O Hasanzadeh… - arXiv preprint arXiv …, 2024 - arxiv.org
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 …
properties and by comparing their behavior with that of the well-known classes of UU rings …
Generalizing Semi--Potent Rings
A Javan, A Moussavi, P Danchev - arXiv preprint arXiv:2501.14632, 2025 - arxiv.org
We define and explore the class of rings $ R $ for which each element in $ R $ is a sum of a
tripotent element from $ R $ and an element from the subring $\Delta (R) $ of $ R $ which …
tripotent element from $ R $ and an element from the subring $\Delta (R) $ of $ R $ which …
Rings with 2-U property
O Hasanzadeh, A Moussavi, P Danchev - arXiv preprint arXiv:2501.04720, 2025 - arxiv.org
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) …
$, where $ J (R)\subseteq\Delta (R)=:\{r\in R| r+ U (R)\subseteq U (R)\} $. The set $\Delta (R) …
Rings such that, for each unit , belongs to the
P Danchev, A Javan, O Hasanzadeh… - arXiv preprint arXiv …, 2024 - arxiv.org
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 $\Delta (R) $ of $ R $ for every unit $ u\in R $. We succeeded to …
n-1$ lies in the subring $\Delta (R) $ of $ R $ for every unit $ u\in R $. We succeeded to …
Group rings that are UJ rings
MT Koşan, J Žemlička - Communications in Algebra, 2021 - Taylor & Francis
The set Δ (R) of all elements r of a ring R such that 1+ ru is a unit for every unit u extends the
Jacobson radical J (R). R is a UJ ring (ΔU ring, respectively) if its units are of the form 1+ J …
Jacobson radical J (R). R is a UJ ring (ΔU ring, respectively) if its units are of the form 1+ J …
Remarks on rings with u− 1 quasi-nilpotent for each unit u
This paper is concerned with the investigation of those rings R whose invertible elements
are sums 1+ a for an element a∈ R such that 1− au is invertible for all invertible u∈ R with …
are sums 1+ a for an element a∈ R such that 1− au is invertible for all invertible u∈ R with …