Action of left identity on <i>n</i> -skew commuting 3-additive mappings

In this paper, our aim is to prove the following result: consider a given integer [Formula: see text], and let [Formula: see text] be a [Formula: see text] torsion free ring possessing a left multiplicative identity e. If [Formula: see text] is a symmetric 3-additive map and [Formula: see text] is the trace of [Formula: see text] such that [Formula: see text] is n-skew commuting on [Formula: see text], then [Formula: see text].