Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism

In this paper we study the variety R2 of square root rings, that is, commutative rings with unit, of characteristic two, with the square root as an additional operation. We prove that this variety is generated by the finite Galois fields GF(2k) and we establish an equivalence between R2 and the variety BAδ of Boolean algebras with a distinguished automorphism. Via this equivalence, we will be able to obtain properties of R2 from the results proved in [M. Abad, J.P. Díaz Varela, M. Zander, Boolean algebras with a distinguished automorphism, Rep. Math. Logic 37 (2003) 101–112].