5 citations · 11 across the 38 of their papers we have counts for
41 papers
-Fine Rings
Peter Danchev, Omid Hasanzadeh, Ahmad Moussavi +1
We introduce and study the so-termed {\it -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 -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 UQ Rings
Peter Danchev, Mina Doostalizadeh, Omid Hasanzadeh
We examine the newly defined class of {\it - rings} described by the condition that for every unit , where denotes the set of quasi-n…
Rings with Clean-Like Properties: Endomorphism, Matrix and Structural Theorems
Adel N. Abyzov, Andrey R. Chekhlov, Peter V. Danchev +1
We investigate three clean-like properties for arbitrary rings, for endomorphism rings of abelian groups and for matrix rings over finite fields. Specifically, we study and establi…
A Generalization of 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 -rings}, hereafter abbreviated as {\it -rings} for short. A ring is said to be $WΔU…
Hereditarily and Super Bassian Modules over Certain Rings
Peter Vassilev Danchev, Truong Cong Quynh, Jan Žemlička
We characterize in certain basic cases when a module over a ring is either {\it hereditarily Bassian} or {\it super Bassian} in the sense that either each its proper submodule is B…
Weakly Rings
Zari Vesali Mahmood, Ahmad Moussavi, Peter Danchev
We introduce and study the so-called {\it weakly rings} (hereafter abbreviated as {\it rings} for short), in which every unit is of the form or …
Rings whose Non-Units are a Unit Multiple of an Element from
Omid Hasanzadeh, Ahmad Moussavi, Peter Danchev
This paper introduces and studies a new class of rings called {\it -rings}. A ring is if every non-unit element can be written as the product of a unit and a…
Rings Such That Lies In For Each Unit
Peter Danchev, Mina Doostalizadeh, Mehrdad Esfandiar +1
We investigate the so-called {\it rings}, a new type of rings in which every unit can be written as with . These rings were defined and studied by S…
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 Strongly \( J^{\#} \)-Clean Rings
Peter Danchev, Gholamreza Karamali, Omid Hasanzadeh +1
We define and examine the class of {\it strongly \( J^{\#} \)-clean rings} consisting of those rings such that each element of is the sum of an idempotent from and an e…
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 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}…
Some Results on Triangular Coefficient Matrix Rings
Peter Danchev, Gholamreza Karamali, Hessam Hosseinnezhad +1
In this paper, we introduce the concept of a {\it triangular coefficient matrix ring} and investigate the structure of its ideals. We then characterize the radicals of the ring \(…
Jordan Derivation On Generalized Triangular Matrix Rings
Peter Danchev, Ayda Fatehi, Masoome Zahiri +1
In this note, we prove that any Jordan derivation on the generalized matrix ring is a derivation. This extends some well-known results of this branch due to Brešar et al…
Matrices over finite fields of odd characteristic as sums of diagonalizable and square-zero matrices
Peter Danchev, Esther García, Miguel Gómez Lozano
Let be a finite field of odd characteristic. When , we prove that every matrix admits a decomposition into where is diagonalizable and…
On Strongly -Clean Rings
Ahmad Moussavi, Peter Danchev, Arash Javan +1
This study explores in-depth the structure and properties of the so-called {\it strongly -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 for Which f.g. Projective Modules Have the FI-extending Property
Peter Danchev, M. Zahiri, S. Zahiri
A right -module is said to be {\it FI-extending} if any fully invariant submodule of is essential in a direct summand of . In this short note we prove that if has…
Some New Classes of Rings Which Have the McCoy Condition
Peter Danchev, M. Zahiri
We define here the notion of a {\it weakly reversible ring} saying that a non-zero element is weakly reversible if there exists an integer depending on such…
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
Peter Danchev, Arash Javan, Omid Hasanzadeh +1
We define and consider in-depth the so-called rings as those rings whose elements are a sum of an element in and of an element in . Our achieved results somew…