On Characterizations of Special Elements in Rings with Involution

Abstract

Let R be a ring with involution. It is well-known that an EP element in R is a core invertible element, but the question when a core invertible element is an EP element, the authors answer in this paper. Several new characterizations of star-core, normal and Hermitian elements in R are also presented.

Keywords

Moore-Penrose inverse / Core inverse / EP element / Star-core element / Normal element / Hermitian element

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