Centralizer’s applications to the inverse along an element Article Swipe

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Inverse Element (criminal law) Mathematics Centralizer and normalizer Inverse problem Inverse element Mathematical analysis Law Geometry Combinatorics Political science Semigroup Special classes of semigroups

Huihui Zhu , Jianlong Chen , Pedro Patrı́cio , Xavier Mary ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.1016/j.amc.2017.07.046 · OA: W2963996157

In this paper, we firstly prove that the absorption law for one-sided inverses along an element holds, and derive the absorption law for the inverse along an element. We then obtain the absorption law for the inverse along different elements. Also, we prove that a left inverse of a along d coincides with a right inverse of a along d, provided that they both exist. Then, the reverse order law and the existence criterion for the inverse along an element are given by centralizers in a ring. Finally, we characterize the Moore–Penrose inverse of a regular element by one-sided invertibilities in a ring with involution.