Rings Whose Elements Are Linear Combinations of Three Commuting Idempotents

Abstract

We classify those rings in which all elements are linear combinations over ℤ of at most three commuting idempotents. Our results improve on recent publications by the author in Albanian J. Math. (2018), Gulf J. Math. (2018), Bull. Iran. Math. Soc. (2018) and Boll. Un. Mat. Ital. (2019) as well as on publications due to Hirano–Tominaga in Bull. Austral. Math. Soc. (1988), Ying et al. in Can. Math. Bull. (2016) and Tang et al. in Lin. and Multilin. Algebra (2019).