Research Article
Pseudo core inverses of a sum of morphisms
DOI:
10.2989/16073606.2020.1791275
Abstract
Let be an additive category with an involution ∗. Suppose that both ϕ : X → X is a morphism of with pseudo core inverse ϕ
and η : X → X is a morphism of such that 1 + ϕ
η is invertible. Let α = (1 + ϕ
η)
−
1
, β = (1+ηϕ
)
−
1
, ε = (1−ϕϕ
)ηα(1−ϕ
ϕ), γ = α(1−ϕ
ϕ)ηϕ
β, σ = αϕ
ϕα−
1(1− ϕϕ
)β, δ = β∗
(ϕ
)
∗η∗
(1−ϕϕ
)β. Then we present a sufficient condition such that f = ϕ + η − ε has pseudo core inverse and give the corresponding expression. Let R be a unital ∗-ring and J(R) its Jacobson radical. If a is pseudo core invertible with the pseudo core inverse a
and j ∈ J(R), we also give a sufficient condition which ensures that a + j − ε has pseudo core inverse. Thus, these results generalize recent results on core inverse.
Get new issue alerts for Quaestiones Mathematicae
