Abstract
We define and examine a new class of rings whose elements are the sum of three commuting idempotents or the difference of two commuting idempotents. We fully describe them up to an isomorphism and our obtained results considerably extend some well-known achievements due to Hirano and Tominaga (Bull Aust Math Soc 37:161–164, 1988), to Ying et al. (Can Math Bull 59:661–672, 2016) and to Tang et al. (Lin Multilin Algebra, 2018).
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