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A familiar way of making one new structure out of two old ones is to form their Cartesian product and, in case the structure involves some algebraic operations, to define the requisite operations coordinatewise. Relation algebras furnish an instance of this procedure. For relation algebras, products come in two flavors: the standard Cartesian (or external) product and an internal version of this product. These two versions are but two sides of the same coin, but each has its own advantages and disadvantages. Products form a critical component in the analysis of relation algebras, and in particular in the reduction of the analysis of complicated algebras to that of simple ones.
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