Relation algebras with n-dimensional relational bases Original Research Article

We study relation algebras with n-dimensional relational bases in the sense of Maddux. Fix n with 3⩽n⩽ω. Write View the MathML source for the class of non-associative algebras with an n-dimensional relational basis, and View the MathML source for the variety generated by View the MathML source. We define a notion of relativised representation for algebras in View the MathML source, and use it to give an explicit (hence recursive) equational axiomatisation of View the MathML source, and to reprove Madduxʹs result that View the MathML source is canonical. We show that the algebras in View the MathML source are precisely those that have a complete relativised representation of this type. Then we prove that whenever 4⩽n