ABSTRACT
As T is generated by the variables x , REG is generated by the elements pp i(x) = -— Pi(x) = p ^ i - i x ) . Now f maps these to the p c( x ) , and so f is cer tainly surjective. But T /R c is the free Boolean algebra generated by the elem ents p c (x), and so there ex ists a homomorphism gj from T /R c to REG mapping p c (x) to pp i(x ). Thus g ^ f is the the identity on the generators of REG and, therefore, on REG itself. Consequently, f is injective and so an iso morphism.
