Given a heterogeneous relation algebra R, it is well-known that the algebra of matrices with coefficients from R is a relation algebra with (not necessarily finite) relational sums. In this paper we want to show that under slightly stronger assumptions the other implication is also true. Every relation algebra R with relational sums and subobjects is equivalent to an algebra of matrices over a suitable basis. This basis is the full subalgebra B induced by the integral objects of R. Integral objects may be characterized by their identity morphisms. Furthermore, we show that this representation is not a trivial one since B is always a proper subalgebra of R. Last but not least, we reprove that every relation algebra may be embedded into a product of simple algebras using our concept of a basis.     «

Given a heterogeneous relation algebra R, it is well-known that the algebra of matrices with coefficients from R is a relation algebra with (not necessarily finite) relational sums. In this paper we want to show that under slightly stronger assumptions the other implication is also true. Every relation algebra R with relational sums and subobjects is equivalent to an algebra of matrices over a suitable basis. This basis is the full subalgebra B induced by the integral objects of R. Integral obje...    »