ABSTRACT
In the previous chapters, we have seen three ways to construct new algebras from given algebras: by formation of subalgebras, quotient algebras, and homomorphic images. In this chapter we examine another important construction, the formation of product algebras. One useful feature of this new construction involves the cardinalities of the algebras obtained. The formation of subalgebras or of homomorphic images of a given algebra leads to algebras with cardinality no larger than the cardinality of the given algebra. The formation of products, however, can lead to algebras with bigger cardinalities than those we started with. There are several ways to define a product of given algebras; we shall examine two products, called the direct product and the subdirect product.
