Geodesic
The rings which are Boolean
Discussiones Mathematicae. General Algebra and Applications, Tome 31 (2011) no. 2, pp. 175-184

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We study unitary rings of characteristic 2 satisfying identity x^p = x for some natural number p. We characterize several infinite families of these rings which are Boolean, i.e., every element is idempotent. For example, it is in the case if p = 2^n - 2 or p = 2^n - 5 or p = 2^n + 1 for a suitable natural number n. Some other (more general) cases are solved for p expressed in the form 2^q + 2m + 1 or 2^q + 2m where q is a natural number and m ∈ 1,2,...,2^q - 1.
Keywords: Boolean ring, unitary ring, characteristic 2 
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Chajda, Ivan; Švrček, Filip. The rings which are Boolean. Discussiones Mathematicae. General Algebra and Applications, Tome 31 (2011) no. 2, pp. 175-184. http://geodesic.mathdoc.fr/item/DMGAA_2011_31_2_a3/