In this paper, we investigate inclusion properties in a ∗-ring. It is proven that for two [Formula: see text]-invertible elements [Formula: see text] and [Formula: see text] in a ∗-ring, [Formula: see text] if and only if [Formula: see text]. For two [Formula: see text]-invertible elements [Formula: see text] and [Formula: see text], [Formula: see text] if and only if [Formula: see text]. Moreover, we give a characterization of [Formula: see text]-inverses, and the absorption law for [Formula: see text]-inverses is studied.
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Lu et al. (2024) studied this question.
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