Axiomatization of identity-free equations valid in relation algebras

A finite axiom set for the identity-free equations valid in relation algebras is given. This is a simplification of the one given by Jonsson, and confirms a conjecture of Tarski. An axiom set for the identity-free equations valid in the representable relation algebras is given, too. We show that in the class of representable relation algebras, both the operation of taking converse and the identity constant are finitely axiomatizable (over the rest of the operations).