A. Moussavi

most citedRings with

u - 1

Quasinilpotent for Each Unit

u

5 citations · 7 across the 6 of their papers we have counts for

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7 papers · 1 filter

math.RA2024

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

Peter Danchev, Arash Javan, Omid Hasanzadeh +2

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 f…

math.RA2024

Rings Whose Non-Invertible Elements are Weakly Nil-Clean

Peter Danchev, Arash Javan, Omid Hasanzadeh +1

In regard to our recent studies of rings with (strongly, weakly) nil-clean-like properties, we explore in-depth both the structural and characterization properties of those rings w…

math.RA2024

Rings whose Non-Invertible Elements are Strongly Nil-Clean

Peter Danchev, Omid Hasanzadeh, Arash Javan +1

We consider in-depth and characterize in certain aspects those rings whose non-units are strongly nil-clean in the sense that they are a sum of commuting nilpotent and idempotent.…

math.RA2024★ 5 cited

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

Peter Danchev, Arash Javan, Omid Hasanzadeh +1

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 an…

math.RA2024★ 1 cited

Rings Whose Clean Elements Are Uniquely Strongly Clean

Peter Danchev, Omid Hasanzadeh, Ahmad Moussavi

We define the class of {\it CUSC} rings, that are those rings whose clean elements are uniquely strongly clean. These rings are a common generalization of the so-called {\it USC} r…

math.RA2024★ 1 cited

Rings Whose Clean and Nil-Clean Elements Have Some Clean-Like Properties

Peter Danchev, Arash Javan, Ahmad Moussavi

We define two types of rings, namely the so-called CSNC and NCUC that are those rings whose clean elements are strongly nil-clean, respectively, whose nil-clean elements are unique…

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

Rings Whose Non-Invertible Elements are Weakly Nil-Clean

Rings whose Non-Invertible Elements are Strongly Nil-Clean

Rings with u−1 Quasinilpotent for Each Unit u

Rings Whose Clean Elements Are Uniquely Strongly Clean

Rings Whose Clean and Nil-Clean Elements Have Some Clean-Like Properties

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

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