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 [Formula: see text], the set of all [Formula: see text] matrices over [Formula: see text], to the set [Formula: see text] of all core-EP invertible elements in an arbitrary unital ring [Formula: see text] with involution. A new partial order is introduced on [Formula: see text] 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.
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