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Rings in Which all Elements are Sums or Differences of Nilpotents and Potents

Rings in Which all Elements are Sums or Differences of Nilpotents and Potents

We examine those rings in which the elements are sums or differences of nilpotents and potents (also including in some special cases tripotents). Such decompositions of matrices over certain rings and fields are also studied. These results of ours somewhat support recent achievements presented in a publication due to Abyzov-Tapkin …