A new class of polar elements in rings

Given a unital ring [Formula: see text] and [Formula: see text]. The element [Formula: see text] is called [Formula: see text]-polar along [Formula: see text] if there exists some [Formula: see text] such that [Formula: see text], [Formula: see text] and [Formula: see text]. Several properties of the [Formula: see text]-polarity along an element are given. Also, a new type of generalized inverses (i.e. the [Formula: see text]-inverse of [Formula: see text] along [Formula: see text]) is defined, and the connection between the [Formula: see text]-polarity along an element and the [Formula: see text]-inverse along an element is established. Finally, [Formula: see text]-JEP elements are introduced and investigated. Several results on the [Formula: see text]-EP element by Yang et al. [Comm. Algebra (2025)] are given as corollaries.