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The rings which are Boolean

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Chajda I., Švrček F.

Discussiones Mathematicae - General Algebra and Applications

2011

tom 31

nr 2

175-184

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 $m ∈ {1,2,...,2^{q} - 1}$.

Ograniczanie wyników

1 Discussiones Mathematicae - General Algebra and Applications

1 Chajda I.

1 Švrček F.

1 2011

Wyniki wyszukiwania

The rings which are Boolean