Properties of core-EP order in rings with involution

Dolinar G., Kuzma B., Marovt J., ÜNGÖR B.

FRONTIERS OF MATHEMATICS IN CHINA, vol.14, no.4, pp.715-736, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.1007/s11464-019-0782-8
  • Journal Name: FRONTIERS OF MATHEMATICS IN CHINA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.715-736
  • Keywords: Drazin inverse, core-EP decomposition, pre-order, ring, INVERSES
  • Ankara University Affiliated: Yes

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 x 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.