A. Moussavi

$Δ$ -Fine Rings

Peter Danchev, Omid Hasanzadeh, Ahmad Moussavi +1

We introduce and study the so-termed {\it $Δ$ -fine rings}, a new class of rings that generalizes the classical {\it fine rings} introduced by Călugăreanu-Lam in J. Algebra \&…

Expanding Generalized Fine Rings

Ahmad Moussavi, Peter Danchev, Arash Javan +1

We introduce and study the so-called {\it generalized $J$ -fine rings}, where every element outside the Jacobson radical is the sum of a unit and an element from the set $\sq…

A Generalization of $Δ$ U Rings

Peter Danchev, Omid Hasanzadeh, Ahmad Moussavi +1

In this paper, we introduce and study a new class of rings calling them {\it weakly $Δ U$ -rings}, hereafter abbreviated as {\it $W Δ U$ -rings} for short. A ring $R$ is said to be $WΔU…

Weakly $J U$ Rings

Zari Vesali Mahmood, Ahmad Moussavi, Peter Danchev

We introduce and study the so-called {\it weakly $J U$ rings} (hereafter abbreviated as {\it $W J U$ rings} for short), in which every unit is of the form $j + 1$ or $j - 1$ …

Rings whose Non-Units are a Unit Multiple of an Element from $Δ (R)$

Omid Hasanzadeh, Ahmad Moussavi, Peter Danchev

This paper introduces and studies a new class of rings called {\it $U Δ$ -rings}. A ring $R$ is $U Δ$ if every non-unit element can be written as the product of a unit and a…

Unit Uniquely Clean Rings

Mina Doostalizadeh, Ahmad Moussavi, Peter Danchev

We define the class of {\it unit uniquely clean} rings ({\it UnitUC} for short), that is a common generalization of uniquely clean rings and strongly nil clean rings. Abelian {\it…

Rings Whose Units Have Identity Plus Quasi-Nilpotent Square

Shahram Najafi, Ahmad Moussavi, Peter Danchev

In this paper, we investigate the structural and characterizing properties of the so-called {\it 2-UQ rings}, that are rings such that the square of every unit is the sum of an ide…

Weakly Strongly 2-Nil-Clean Rings

Peter Danchev, Mina Doostalizadeh, Ahmad Moussavi

In this paper, we introduce and explore in-depth the notion of {\it weakly strongly 2-nil-clean rings} as a common non-trivial generalization of both strongly 2-nil-clean rings and…

On Rings with the 2-UNJ Property

Zari Vesali Mahmood, Ahmad Moussavi, Peter Danchev

In this paper, we introduce a new class of rings calling them {\it 2-UNJ rings}, which generalize the well-known 2-UJ, 2-UU and UNJ rings. Specifically, a ring $R$ is called 2-UNJ…

Rings Whose Non-Units are Square-Nil Clean

Mina Doostalizadeh, Ahmad Moussavi, Peter Danchev

We consider in-depth and characterize in certain aspects the class of so-called {\it strongly NUS-nil clean rings}, that are those rings whose non-units are {\it square nil-clean}…

On Strongly $Δ$ -Clean Rings

Ahmad Moussavi, Peter Danchev, Arash Javan +1

This study explores in-depth the structure and properties of the so-called {\it strongly $Δ$ -clean rings}, that is a novel class of rings in which each ring element decomposes into…

A New Characterization of Semi-Tripotent Rings

Ahmad Moussavi, Peter Danchev, Arash Javan +1

We give a comprehensive study of the so-called \textit{semi-tripotent rings} obtaining their new and non-trivial characterization as well as a complete description in terms of sums…

Rings Whose Non-Invertible Elements are Strongly Weakly Nil-Clean

Peter Danchev, Mina Doostalizadeh, Omid Hasanzadeh +2

The target of the present work is to give a new insight in the theory of {\it strongly weakly nil-clean} rings, recently defined by Kosan and Zhou in the Front. Math. China (2016)…

Rings in which all elements are the sum of a central element and an element from $Δ (R)$

Peter Danchev, Arash Javan, Omid Hasanzadeh +1

We define and consider in-depth the so-called $C Δ$ rings as those rings $R$ whose elements are a sum of an element in $C (R)$ and of an element in $Δ (R)$ . Our achieved results somew…

Generalizing Semi- $n$ -Potent Rings

Arash Javan, Ahmad Moussavi, Peter Danchev

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 $Δ (R)$ of $R$ which commute each…

Rings with 2- $Δ$ U property

Omid Hasanzadeh, Ahmad Moussavi, Peter Danchev

Rings in which the square of each unit lies in $1 + Δ (R)$ , are said to be $2$ - $Δ U$ , where $J (R) \subseteq Δ (R) =: {r \in R ∣ r + U (R) \subseteq U (R)}$ . The set $Δ (R)$ is the largest…

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…

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…

Rings Whose Non-Invertible Elements Are Nil-Clean

Peter Danchev, Arash Javan, Omid Hasanzadeh +1

We systematically study those rings whose non-units are a sum of an idempotent and a nilpotent. Some crucial characteristic properties are completely described as well as some stru…

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…