8 citations · 16 across the 27 of their papers we have counts for
29 papers
Generalized right group inverse in Banach *-algebras
Huanyin Chen, Marjan Sheibani
In this paper, we introduce the concept of the generalized right group inverse within the context of a *-Banach algebra. This represents a natural extension of the generalized (wea…
The -generalized right group inverses in Banach algebras
Huanyin Chen, Marjan Sheibani
In this paper, we introduce the concept of the m-generalized right group inverse. This serves as a natural extension of both the m-weak group inverse and the generalized group inve…
New properties of weighted generalized core-EP inverse in Banach algebras
Huanyin Chen, Marjan Sheibani
We characterize the generalized weighted core-EP inverse via the canonical decomposition, utilizing a weighted core-EP invertible element and a quasinilpotent. We then offer a pola…
On generalized core-EP invertibility in a Banach algebra
Huanyin Chen, Marjan Sheibani
We present new properties of generalized core-EP inverse in a Banach *-algebra. We characterize this new generalized inverse by using involved annihilators. The generalized core-EP…
New additive results of *-DMP elements on Banach algebras
Ali Ghaffari, Fatemeh Zamiri, Marjan Sheibani
We present new additive results for DMP elements in a Banach algebra with involution. The necessary and sufficient conditions under which the sum of two DMP elements is DMP are inv…
G-Drazin inverse and group inverse for the anti-triangular block-operator matrices
Huanyin Chen, Marjan Sheibani
We present the generalized Drazin inverse for certain anti-triangular operator matrices. Let . If and , we prove that $M=\left(…
The g-Drazin inverses of anti-triangular block operator matrices
Huanyin Chen, Marjan Sheibani
An element in a Banach algebra has g-Drazin inverse if there exists such that and . In this paper…
Pseudo core invertibility in Banach *-algebras and its applications
Huanyin Chen, Marjan Sheibani
We present new additive results for the pseudo core inverse in a Banach algebra with involution. The necessary and sufficient conditions under which the sum of two pseudo core inve…
The Core Inverse in a Banach Algebra with Involution
Marjan Sheibani, Huanyin Chen
We present new additive results for the core inverse in a Banach algebra with involution. We obtain necessary and sufficient conditions under which the sum of two core invertible e…
Group inverse for anti-triangular block operator matrices
Huanyin Chen, Marjan Sheibani
We present the existence of the group inverse and its representation for the block operator matrix under the condition $FEF…
The group inverse of the sum in a Banach algebra
Huanyin Chen, Marjan Sheibani
In this paper, we present new necessary and sufficient conditions under which the sum of two group invertible elements in a Banach algebra has group inverse. We then apply these re…
Group invertibility of the sum in rings and its applications
Huanyin Chen, Dayong Liu, Marjan Sheibani
We present new additive results for the group invertibility in a ring. Then we apply our results to block operator matrices over Banach spaces and derive the existence of group inv…
The g-Drazin invertibility in a Banach algebra
Huanyin Chen, Marjan Sheibani
We present necessary and sufficient conditions under which the anti-triangular matrix over a Banach algebra has g-Drazin inve…
Generalized Cline's formula and Jacobson's lemma in a ring
Huanyin Chen, Marjan Sheibani
We present new generalized Cline's formula and Jacobson's lemma for the g-Drazin inverse in a ring. These extend many known results, e.g., Chen and Abdolyousefi (Generalized Jacobs…
Generalized Jacobson's lemma for generalized Drazin inverses
Huanyin Chen, Marjan Sheibani
We present new generalized Jacobson's lemma for generalized Drazin inverses. This extend the main results on g-Drazin inverse of Yan, Zeng and Zhu (Linear Multilinear Algebra,…
Jacobson's Lemma for the generalized n-strongly Drazin inverse
Huanyin Chen, Marjan Sheibani
Let . An element has generalized n-strongly Drazin inverse if there exists such that For any $a,b\in R…
Expressions for the g-Drazin inverse in a Banach algebra
Huanyin Chen, Marjan Sheibani
We explore the generalized Drazin inverse in a Banach algebra. Let be a Banach algebra, and let . If then $a+b\in \mathcal{A}^{…
Additive properties of G-Drazin inverse of linear operators
Huanyin Chen, Marjan Sheibani
In this paper, we investigate additive properties of generalized Drazin inverse for linear operators in Banach spaces. Under new polynomial conditions on generalized Drazin inverti…
On Hirano inverses in rings
Huanyin Chen, Marjan Sheibani
We introduce and study a new class of Drazin inverses. An element in a ring has Drazin inverse if , and . Every Hirano inverse of an elem…
Generalized Hirano inverses in rings
Marjan Sheibani Abdolyousefi, Huanyin Chen
We introduce and study a new class of generalized inverse in rings. An element in a ring has generalized Hirano inverse if there exists some such that $bab=b, b\in…
Rings over which every matrix is the sum of a tripotent and a nilpotent
M Sheibani, H Chen
A ring is trinil clean if every element in is the sum of a tripotent and a nilpotent. If is a 2-primal strongly 2-nil-clean ring, we prove that is trinil clean…
Rings over which every matrix is the sum of two idempotents and a nilpotent
H. Chen, M. Sheibani
A ring is (strongly) 2-nil-clean if every element in is the sum of two idempotents and a nilpotent (that commute). Fundamental properties of such rings are discussed. Let $…
Elementary matrix reduction over Bezout duo rings
Huanyin Chen, Marjan Sheibani
A ring is an elementary divisor ring if every matrix over admits a diagonal reduction. We further explore various stable like conditions on a bezout duo-domain under which…
Refinement rings, localization and diagonal reduction of matrices
Nahid Ashrafi, Rahman Bahmani Sangesari, Marjan Sheibani
In this paper we prove that if is a commutative refinement ring and , are two -modules then, if and only if for every maximal ideal of , $M_m\cong N…