A. Javan

activity

20242026

collaborators

Showing 2024Show all

8 papers · 1 filter

math.RA2024

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

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 $I^ (R)$ of $R$ for every unit $u \in R$ . We succeeded to describe…

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 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…

math.RA2024

On Some Extensions of $I ¨ $ -Regular Rings

Peter Danchev, Arash Javan, Ahmad Moussavi

Some variations of $I ¨ $ -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…

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

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…

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

Rings Whose Non-Invertible Elements are Weakly Nil-Clean

Rings Whose Non-Invertible Elements Are Nil-Clean

On Some Extensions of I¨-Regular Rings

Rings whose Non-Invertible Elements are Strongly Nil-Clean

Rings with u−1 Quasinilpotent for Each Unit u

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

On Some Extensions of $I ¨ $ -Regular Rings

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