5 citations · 11 across the 38 of their papers we have counts for
12 papers · 1 filter
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…
Two-Term Polynomial Identities
Allan Berele, Peter Danchev, Bridget Eileen Tenner
We study algebras satisfying a two-term multilinear identity, namely one of the form , where is a parameter from the base field. We…
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.…
Decompositions of Periodic Matrices into a Sum of Special Matrices
Peter Danchev, Esther García, Miguel Gómez Lozano
We study the problem of when a periodic square matrix of order over an arbitrary field is decomposable into the sum of a square-zero matrix and a torsion matrix, a…
On prescribed characteristic polynomials
Peter Danchev, Esther García, Miguel Gómez Lozano
Let be a field. We show that given any th degree monic polynomial and any matrix whose trace coincides with t…
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…
Rings Whose Non-Invertible Elements Are Uniquely Strongly Clean
Peter Danchev, Mehrdad Esfandiar, Omid Hasanzadeh
We define and investigate in details the class of so-termed {\it GUSC} rings, that are those rings whose non-invertible elements are uniquely strongly clean. These rings are a comm…