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arXiv · 1804.08820

The core and dual core inverses of morphisms with kernels

Tingting Li·Jianlong Chen·Mengmeng Zhou·Dingguo Wang
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Abstract

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 $\kappa\lambda$ 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.

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Tingting Li, Jianlong Chen, Mengmeng Zhou, Dingguo Wang. 2018-04-24. The core and dual core inverses of morphisms with kernels. https://arxiv.org/abs/1804.08820

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