2011•Discussiones Mathematicae - General Algebra and ApplicationsOpen access
The rings which are Boolean
Ivan Chajda, Filip Švrček
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Abstract
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}.
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