The rings which are Boolean (Q2906344)

The authors aim to get properties of unitary rings of characteristic 2 satisfying the identity \(x^p = x\) for some natural number \(p\), characterizing some classes of such rings whose elements are idempotent. These classes are determined by the properties of the number \(p\) (\(p = 2^{n-2}\) and \(n\) bigger than 1, \(p = 2^{n-5}\) and \(n\) bigger than \(3\) and so on). Some results confirm that there are cases of \(p\) for which the rings are not Boolean (for example, in Lemma 3, \(p = 3k+1\)). Some examples of both cases (Boolean or not) are also given in the paper.