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The rings which are Boolean. II. (English) Zbl 1276.16034
Summary: We answer the following question: if one has a ring $$R$$ of characteristic 2 satisfying $$x^p=x$$, for some $$p$$; which values of $$p$$ imply the identity $$x^2=x$$?
For part I see I. Chajda and F. Švrček [Discuss. Math., Gen. Algebra Appl. 31, No. 2, 175-184 (2011; Zbl 1262.06005)].
##### MSC:
 16U80 Generalizations of commutativity (associative rings and algebras) 06E20 Ring-theoretic properties of Boolean algebras 16R40 Identities other than those of matrices over commutative rings 16N40 Nil and nilpotent radicals, sets, ideals, associative rings 16U70 Center, normalizer (invariant elements) (associative rings and algebras) 16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
##### Keywords:
Boolean rings; unitary rings; characteristic 2