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Outer inverses belonging to the prescribed Green’s equivalence classes in an involutive semigroup
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Outer inverses belonging to the prescribed Green’s equivalence classes in an involutive semigroup
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Journal Article
Outer inverses belonging to the prescribed Green’s equivalence classes in an involutive semigroup
2025
Overview
We provide existence criteria and characterizations for outer inverses in an involutive semigroup belonging to the prescribed Green’s
R
-,
L
- and
H
-classes. We show that the existence criteria for such outer inverses are simultaneously the existence criteria for various types of generalized inverses, such as
{
1
,
4
}
-inverses,
{
1
,
3
}
-inverses, Moore–Penrose inverses, core inverses and dual core inverses. We also provide several new characterizations of the mentioned types of generalized inverses, as well as characterizations of
{
2
,
4
}
-inverses and
{
2
,
3
}
-inverses.
Publisher
Springer US,Springer Nature B.V
Subject
