scholarly journals The perturbation of the group inverse under the stable perturbation in a unital ring

Filomat ◽  
2013 ◽  
Vol 27 (1) ◽  
pp. 65-74 ◽  
Author(s):  
Fapeng Du ◽  
Yifeng Xue
Keyword(s):  
Group Inverse ◽  
Unital Ring ◽  
Stable Perturbation

scholarly journals On group invertibility in rings

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6141-6150
Author(s):  
Nadica Mihajlovic ◽  
Dragan Djordjevic
Keyword(s):  
Linear Algebra ◽  
Group Inverse ◽  
Unital Ring

We prove some results for the group inverse of elements in a unital ring. Thus, some results from (C. Deng, Electronic J. Linear Algebra 31 (2016)) are extended to more general settings.

scholarly journals Functional identities on upper triangular matrix rings

2020 ◽  
Vol 18 (1) ◽  
pp. 182-193
Author(s):  
He Yuan ◽  
Liangyun Chen
Keyword(s):  
Triangular Matrix ◽  
Matrix Rings ◽  
Unital Ring ◽  
Functional Identities ◽  
Upper Triangular Matrix ◽  
Free Subset

Abstract Let R be a subset of a unital ring Q such that 0 ∈ R. Let us fix an element t ∈ Q. If R is a (t; d)-free subset of Q, then Tn(R) is a (t′; d)-free subset of Tn(Q), where t′ ∈ Tn(Q), $\begin{array}{} t_{ll}' \end{array} $ = t, l = 1, 2, …, n, for any n ∈ N.

Solving fuzzy linear systems using a block representation of generalized inverses: The group inverse

2018 ◽  
Vol 353 ◽  
pp. 66-85 ◽  
Author(s):  
Biljana Mihailović ◽  
Vera Miler Jerković ◽  
Branko Malešević
Keyword(s):  
Linear Systems ◽  
Generalized Inverses ◽  
Group Inverse ◽  
Fuzzy Linear Systems

Commutative rings and modules that are Nil*-coherent or special Nil*-coherent

2017 ◽  
Vol 16 (10) ◽  
pp. 1750187 ◽  
Author(s):  
Karima Alaoui Ismaili ◽  
David E. Dobbs ◽  
Najib Mahdou
Keyword(s):  
Commutative Rings ◽  
Finitely Generated ◽  
Basic Properties ◽  
Unital Ring ◽  
Reduced Ring ◽  
Coherent Ring ◽  
Ring Extensions ◽  
Coherent Rings ◽  
Finitely Presented

Recently, Xiang and Ouyang defined a (commutative unital) ring [Formula: see text] to be Nil[Formula: see text]-coherent if each finitely generated ideal of [Formula: see text] that is contained in Nil[Formula: see text] is a finitely presented [Formula: see text]-module. We define and study Nil[Formula: see text]-coherent modules and special Nil[Formula: see text]-coherent modules over any ring. These properties are characterized and their basic properties are established. Any coherent ring is a special Nil[Formula: see text]-coherent ring and any special Nil[Formula: see text]-coherent ring is a Nil[Formula: see text]-coherent ring, but neither of these statements has a valid converse. Any reduced ring is a special Nil[Formula: see text]-coherent ring (regardless of whether it is coherent). Several examples of Nil[Formula: see text]-coherent rings that are not special Nil[Formula: see text]-coherent rings are obtained as byproducts of our study of the transfer of the Nil[Formula: see text]-coherent and the special Nil[Formula: see text]-coherent properties to trivial ring extensions and amalgamated algebras.

Group inverse sampling: An economical approach to inverse sampling

2017 ◽  
Vol 28 (7) ◽  
pp. e2459 ◽  
Author(s):  
Bardia Panahbehagh ◽  
David R. Smith
Keyword(s):  
Group Inverse ◽  
Inverse Sampling

scholarly journals A commutativity theorem for lefts-unital rings

1990 ◽  
Vol 13 (4) ◽  
pp. 769-774
Author(s):  
Hamza A. S. Abujabal
Keyword(s):  
Commutativity Theorem ◽  
Unital Ring ◽  
Commutativity Theorems ◽  
Associative Rings ◽  
Unital Rings

In this paper we generalize some well-known commutativity theorems for associative rings as follows: LetRbe a lefts-unital ring. If there exist nonnegative integersm>1,k≥0, andn≥0such that for anyx,yinR,[xky−xnym,x]=0, thenRis commutative.

scholarly journals On commutativity of one-sideds-unital rings

1992 ◽  
Vol 15 (4) ◽  
pp. 813-818
Author(s):  
H. A. S. Abujabal ◽  
M. A. Khan
Keyword(s):  
Polynomial Identity ◽  
Unital Ring ◽  
Unital Rings

The following theorem is proved: Letr=r(y)>1,s, andtbe non-negative integers. IfRis a lefts-unital ring satisfies the polynomial identity[xy−xsyrxt,x]=0for everyx,y∈R, thenRis commutative. The commutativity of a rights-unital ring satisfying the polynomial identity[xy−yrxt,x]=0for allx,y∈R, is also proved.

scholarly journals On Stable Perturbations of the Generalized Drazin Inverses of Closed Linear Operators in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Qianglian Huang ◽  
Lanping Zhu ◽  
Xiaoru Chen ◽  
Chang Zhang
Keyword(s):  
Banach Spaces ◽  
Null Space ◽  
Linear Operators ◽  
Special Cases ◽  
Stable Perturbation ◽  
Closed Linear Operators

We investigate the stable perturbation of the generalized Drazin inverses of closed linear operators in Banach spaces and obtain some new characterizations for the generalized Drazin inverses to have prescribed range and null space. As special cases of our results, we recover the perturbation theorems of Wei and Wang, Castro and Koliha, Rakocevic and Wei, Castro and Koliha and Wei.

scholarly journals Group inverse matrix of the normalized Laplacian on subdivision networks

2020 ◽  
pp. 23-23
Author(s):  
Ángeles Carmona ◽  
Margarida Mitjana ◽  
Enric Monsó
Keyword(s):  
Inverse Matrix ◽  
Group Inverse ◽  
Kirchhoff Index ◽  
Base Network

In this paper we consider a subdivision of a given network and we show how the group inverse matrix of the normalized laplacian of the subdivision network is related to the group inverse matrix of the normalized laplacian of the initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both structures and takes advantage on the properties of the group inverse matrix. As a consequence we get formulae for effective resistances and the Kirchhoff Index of the subdivision network expressed in terms of its corresponding in the base network. Finally, we study two examples where the base network are the star and the wheel, respectively.

Sign in / Sign up

Export Citation Format

Share Document