The connection of skew Boolean algebras and discriminator varieties to Church algebras
نویسندگان
چکیده
We establish a connection between skew Boolean algebras and Church algebras. We prove that the set of all semicentral elements in a right Church algebra forms a right-handed skew Boolean algebra for the properly defined operations. The main result of this paper states that the variety of all semicentral right Church algebras of type τ is term equivalent to the variety of right-handed skew Boolean algebras with additional regular operations. As a corollary to this result we show that a pointed variety is a discriminator variety if and only if it is a 0-regular variety of right-handed skew Boolean algebras.
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