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The rings which are Boolean

Ivan Chajda, Filip Švrček (2011)

Discussiones Mathematicae - General Algebra and Applications

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 + 2 m + 1 or 2 q + 2 m where q is a natural number and m 1 , 2 , . . . , 2 q - 1 .

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