On generalized inverses and Green's relations
By Xavier Mary. 2009
146 citations recorded by the source corpus.
We study generalized inverses on semigroups by means of Green's relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse and Moore-Penrose inverse) belong to this class.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/1824c893f190eacdff46d4670374bfd72cd52380
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Arturas Stikonas
- Jianlong Chen
- Pedro Patrício
- Tingting Li
- Enrico Boasso
- Julio Benítez
- Hongwei Jin
- Huihui Zhu
In Computational Theory and Mathematics
- Jianlong Chen
- Arturas Stikonas
- Pedro Patrício
- Tingting Li
- Dragan S. Djordjevi'c
- Xavier Mary
- Enrico Boasso
- Julio Benítez
Citations in the corpus
- Pseudo core inverses in rings with involution (2016, unknown): “For a, b ∈ R, a ≤H b ⇔ Ra ⊆ Rb and aR ⊆ bR [13].”
- Further results on the inverse along an element in semigroups and rings (2016, background): “Mary [6] recently defined a new generalized inverse in a semigroup S called the inverse along an element.”
- ON ONE-SIDED (B;C)-INVERSES OF ARBITRARY MATRICES (2017, background): “To learn more on this inverse, see [3, 4, 15, 16].”
- Generalized inverses modulo ℋ in semigroups and rings (2013, methodology): “A new existence criterion In [11], the existence of an inverse of a along d was related to the existence of certain group inverses.”
- Group, Moore–Penrose, core and dual core inverse in rings with involution☆ (2014, background): “In Section 4, we will show that considered inverses belong to the class of inverses along an element, introduced by Mary in [9] and to the class of outer generalized inverses introduced by Drazin in [7].”
- Characterizations of core and dual core inverses in rings with involution (2016, background): “Mary [11] told us that a# = a‖a and a† = a‖a .”
- A survey on stationary problems, Green’s functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions (2014, methodology): “In [135], a new class of generalized inverses on semigroups was introduced by means of Green’s relations.”