scholarly journals Generalized inverses over integral domains. II. group inverses and Drazin inverses

1991 ◽  
Vol 146 ◽  
pp. 31-47 ◽  
Author(s):  
K. Manjunatha Prasad ◽  
K.P.S. Bhaskara Rao ◽  
R.B. Bapat
Keyword(s):  
Generalized Inverses ◽  
Integral Domains ◽  
Group Inverses

On the uniform boundedness and convergence of generalized, Moore-Penrose and group inverses

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5993-6003 ◽  
Author(s):  
Lanping Zhu ◽  
Changpeng Zhu ◽  
Qianglian Huang
Keyword(s):  
Operator Theory ◽  
Generalized Inverse ◽  
Matrix Theory ◽  
Uniform Boundedness ◽  
Generalized Inverses ◽  
Convergence Theorems ◽  
Linear Subspaces ◽  
Group Inverses ◽  
Stable Perturbation ◽  
The Relationship

This paper concerns the relationship between uniform boundedness and convergence of various generalized inverses. Using the stable perturbation for generalized inverse and the gap between closed linear subspaces, we prove the equivalence of the uniform boundedness and convergence for generalized inverses. Based on this, we consider the cases for the Moore-Penrose inverses and group inverses. Some new and concise expressions and convergence theorems are provided. The obtained results extend and improve known ones in operator theory and matrix theory.

scholarly journals Generalized inverses over integral domains

1990 ◽  
Vol 140 ◽  
pp. 181-196 ◽  
Author(s):  
R.B. Bapat ◽  
K.P.S. Bhaskara Rao ◽  
K.Manjunatha Prasad
Keyword(s):  
Generalized Inverses ◽  
Integral Domains

scholarly journals Generalized inverses and their relations with clean decompositions

2019 ◽  
Vol 18 (07) ◽  
pp. 1950133 ◽  
Author(s):  
Huihui Zhu ◽  
Honglin Zou ◽  
Pedro Patrício
Keyword(s):  
Positive Integer ◽  
Generalized Inverses ◽  
Decomposition Formula ◽  
Group Inverses ◽  
Unit Formula

An element [Formula: see text] in a ring [Formula: see text] is called clean if it is the sum of an idempotent [Formula: see text] and a unit [Formula: see text]. Such a clean decomposition [Formula: see text] is said to be strongly clean if [Formula: see text] and special clean if [Formula: see text]. In this paper, we prove that [Formula: see text] is Drazin invertible if and only if there exists an idempotent [Formula: see text] and a unit [Formula: see text] such that [Formula: see text] is both a strongly clean decomposition and a special clean decomposition, for some positive integer [Formula: see text]. Also, the existence of the Moore–Penrose and group inverses is related to the existence of certain ∗-clean decompositions.

scholarly journals Decomposition and classification of length functions

2020 ◽  
Vol 32 (5) ◽  
pp. 1109-1129
Author(s):  
Dario Spirito
Keyword(s):  
Integral Domain ◽  
Integral Domains ◽  
Bijective Correspondence ◽  
Length Functions ◽  
Standard Representation ◽  
Prufer Domains ◽  
Prüfer Domains

AbstractWe study decompositions of length functions on integral domains as sums of length functions constructed from overrings. We find a standard representation when the integral domain admits a Jaffard family, when it is Noetherian and when it is a Prüfer domains such that every ideal has only finitely many minimal primes. We also show that there is a natural bijective correspondence between singular length functions and localizing systems.

Test matrices for generalized inverses

1978 ◽  
Vol 13 (4) ◽  
pp. 10-12 ◽  
Author(s):  
Gerhard Zielke
Keyword(s):  
Generalized Inverses ◽  
Test Matrices
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