Abstract
The concept of internally cancellable rings has been extensively studied in the literature. This paper seeks to continue the study of these rings and find some new characterizations. It is proved that [Formula: see text] is “IC”, if and only if for each regular element [Formula: see text], and idempotent element [Formula: see text] with [Formula: see text], there exists [Formula: see text] such that [Formula: see text] is a unit (alternatively, unit-regular element) in [Formula: see text] and [Formula: see text]. In case the ring [Formula: see text] has the summand sum property, we indicate that [Formula: see text] is IC, if and only if for each regular element [Formula: see text], and element [Formula: see text] with [Formula: see text], there exists an idempotent [Formula: see text], such that [Formula: see text] is a unit in [Formula: see text] and [Formula: see text].
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