Properties of core-EP order in rings with involution

Abstract

We study properties of a relation in *-rings, called the core-EP (pre)order which was introduced by H. Wang on the set of all n × n complex matrices [Linear Algebra Appl., 2016, 508: 289–300] and has been recently generalized by Y. Gao, J. Chen, and Y. Ke to *-rings [Filomat, 2018, 32: 3073–3085]. We present new characterizations of the core-EP order in *-rings with identity and introduce the notions of the dual core-EP decomposition and the dual core-EP order in-rings.

Keywords

Drazin inverse / core-EP decomposition / pre-order / ring

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