Algebraic analysis demonstrates characterizations of rings where containment relations among regular element classes collapse to equalities, indicating refined structural classifications.
Let [Formula: see text] denote the set of all the strongly regular elements of a unital ring [Formula: see text], [Formula: see text] the set of all the unit-regular elements of [Formula: see text] and [Formula: see text] the set of all the stable range one elements of [Formula: see text]. It is well-known that [Formula: see text], where [Formula: see text] denotes the group of units of [Formula: see text]. In this note we characterize rings for which some of these inclusions become equalities, either individually or collectively.
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Grigore Calugareanu (2026) studied this question.
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