A New Characterization of Semi-Tripotent Rings

We give a comprehensive study of the so-called $\mathit{\text{semi-tripotent}}\mathit{\text{rings}}$ obtaining their new and non-trivial characterization as well as a complete description in terms of sums and products of some special elements. Particularly, we explore in-depth when a group ring is semi-tripotent. Our results somewhat supply those established by Ko$\stackrel{\backslash c}{s}$an et al. in Can. Math. Bull. (2019).