Rings Whose Elements are Sums of Three or Differences of Two Commuting Idempotents
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).
KeywordsBoolean rings Units Idempotents Nilpotents Jacobson radical
Mathematics Subject Classification16D 60 16S 34 16U 60
The author would like to express his sincere thanks to the specialist referee for the professional comments and suggestions on the submitted paper and, especially, for indicating the existence of the manuscript .
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