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On some orders in ∗-rings based on the core-EP decomposition

Janko Marovt

University of Maribor, Faculty of Economics and Business, Razlagova 14, SI-2000 Maribor, Slovenia

IMFM, Jadranska 19, SI-1000 Ljubljana, Slovenia

E-mail Address: janko.marovt@um.si

Corresponding author.

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and

Dijana Mosić

Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000 Niš, Serbia

E-mail Address: dijana@pmf.ni.ac.rs

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https://doi.org/10.1142/S0219498822500104Cited by:4 (Source: Crossref)

Abstract

We study certain relations in unital rings with involution that are derived from the core-EP decomposition. The notion of the WG pre-order and the C-E partial order is extended from $M_{n} (ℂ)$ , the set of all $n \times n$ matrices over $ℂ$ , to the set $ℛ^{ⓓ}$ of all core-EP invertible elements in an arbitrary unital ring $ℛ$ with involution. A new partial order is introduced on $ℛ^{ⓓ}$ by combining the WG pre-order and the well known minus partial order, and a new characterization of the core-EP pre-order in unital proper ∗-rings is presented. Properties of these relations are investigated and some known results are thus generalized.

Communicated by S. K. Jain

Keywords:

AMSC: 06F25, 06A06, 15A09

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