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Let $mathscr{C}$ be an additive category with an involution $ast$. Suppose that $varphi : X rightarrow X$ is a morphism with kernel $kappa : K rightarrow X$ in $mathscr{C}$, then $varphi$ is core invertible if and only if $varphi$ has a cokernel $lambda: X rightarrow L$ and both $kappalambda$ and $varphi^{ast}varphi^3+kappa^{ast}kappa$ are invertible. In this case, we give the representation of the core inverse of $varphi$. We also give the corresponding result about dual core inverse.
Let $mathscr{C}$ be an additive category with an involution $ast$. Suppose that $varphi : X rightarrow X$ is a morphism of $mathscr{C}$ with core inverse $varphi^{co} : X rightarrow X$ and $eta : X rightarrow X$ is a morphism of $mathscr{C}$ such tha
Let R be a unital ring with involution, we give the characterizations and representations of the core and dual core inverses of an element in R by Hermitian elements (or projections) and units. For example, let a in R and n is an integer greater than
In this paper, we introduce two new generalized inverses of matrices, namely, the $bra{i}{m}$-core inverse and the $pare{j}{m}$-core inverse. The $bra{i}{m}$-core inverse of a complex matrix extends the notions of the core inverse defined by Baksalar
Let $mathscr{C}$ be a category with an involution $ast$. Suppose that $varphi : X rightarrow X$ is a morphism and $(varphi_1, Z, varphi_2)$ is an (epic, monic) factorization of $varphi$ through $Z$, then $varphi$ is core invertible if and only if $(v
In this paper, we introduce the notion of a (generalized) right core inverse and give its characterizations and expressions. Then, we provide the relation schema of (one-sided) core inverses, (one-sided) pseudo core inverses and EP elements.