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We completely determine up to isomorphism those rings whose elements x have the specific property that x or −x is a sum of three commuting idempotents. This statement strengthens well-known results in the subject due to Hirano-Tominaga (Bull. Austral. Math. Soc., 1988), Ying et al. (Can. Math. Bull., 2016), Tang et al. (Lin. & Multilin. Algebra, 2018), Danchev (Boll. Un. Mat. Ital., 2019) and (Bull. Iran. Math. Soc., 2019).

Rings whose elements are sums or minus sums of three commuting idempotents