Comments are welcome.
I show that the class of full Peirce algebras is characterised by the class of complete and atomic Peirce algebras in which the set of relational atoms is restricted by two conditions. One requires simplicity. The other requires that each relational element can be uniquely expressed in terms of Boolean atoms, or equivalently, that each relational element can be uniquely expressed in terms of relational identity atoms or relational points. To this end I investigate the interrelationship of identity elements and right ideal elements inside any relation algebra and the interrelationship of identity elements, right ideal elements and Boolean set elements inside Peirce algebras. Each form a Boolean algebra.