Quotient Semiproducts

Abstract

Quotient semiproducts constitute a substantial generalization of the semipower construction of Chapter 4 In the latter, a single simple relation algebra is given, and bijections are used to make isomorphic copies of this base algebra in every component of a corresponding rectangular system. In the quotient semiproduct construction, there is not a single base algebra, but rather a system of base algebras, and equijections are used to make isomorphic copies, not of the base algebras, but of quotients of the base algebras. (A base algebra can, itself, be such a quotient, namely the quotient by the identity element.) Moreover, the various copies of a given base algebra need not be copies of the same quotient. This provides a good deal of flexibility in the construction, and allows for a much greater variety of structure within and between the various components of the final semiproduct than is possible in the semipower construction (Figure 8.1).