Frontiers of Mathematics in China >

2019 , Vol. 14 >Issue 4: 715 - 736

DOI: https://doi.org/10.1007/s11464-019-0782-8

RESEARCH ARTICLE

Properties of core-EP order in rings with involution

  • Gregor DOLINAR 1,4 ,
  • Bojan KUZMA 2,4 ,
  • Janko MAROVT , 3,4 ,
  • Burcu UNGOR 5
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  • 1. University of Ljubljana, Faculty of Electrical Engineering, Trzaska 25, SI-1000 Ljubljana, Slovenia
  • 2. University of Primorska, Glagoljaska 8, SI-6000 Koper, Slovenia
  • 3. University of Maribor, Faculty of Economics and Business, Razlagova 14, SI-2000 Maribor, Slovenia
  • 4. IMFM, Jadranska 19, SI-1000 Ljubljana, Slovenia
  • 5. Faculty of Sciences, Ankara University, 06100, Tandogan, Ankara, Turkey

Received date: 16 May 2018

Accepted date: 28 Jul 2019

Published date: 15 Aug 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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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.

Key words： Drazin inverse; core-EP decomposition; pre-order; ring

Cite this article

Gregor DOLINAR , Bojan KUZMA , Janko MAROVT , Burcu UNGOR . Properties of core-EP order in rings with involution[J]. Frontiers of Mathematics in China, 2019 , 14(4) : 715 -736 . DOI: 10.1007/s11464-019-0782-8

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