5 citations · 7 across the 16 of their papers we have counts for
17 papers · 1 filter
-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…
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 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…
Generalizing Semi--Potent Rings
Arash Javan, Ahmad Moussavi, Peter Danchev
We define and explore the class of rings for which each element in is a sum of a tripotent element from and an element from the subring of which commute each…
Rings such that, for each unit , belongs to the
Peter Danchev, Arash Javan, Omid Hasanzadeh +2
We study in-depth those rings for which, there exists a fixed , such that lies in the subring of for every unit . 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.…
Rings with Quasinilpotent for Each Unit
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…
Rings Whose Invertible Elements Are Weakly Nil-Clean
Peter Danchev, Omid Hasanzadeh, Arash Javan +1
We study those rings in which all invertible elements are weakly nil-clean calling them {\it UWNC rings}. This somewhat extends results due to Karimi-Mansoub et al. in Contemp. Mat…
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…
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…
On Some Extensions of -Regular Rings
Peter Danchev, Arash Javan, Ahmad Moussavi
Some variations of -regular and nil clean rings were recently introduced in \cite{5,8,7}, respectively. In this paper, we examine the structure and relationships between these c…
Rings With Nilpotent For Each Unit
Peter Danchev, Arash Javan, Ahmad Moussavi
We continue the study in-depth of the so-called -UU rings for any , that were defined by the first-named author in Toyama Math. J. (2017) as those rings for which $…