Abstract

Publisher Summary The chapter describes the techniques used to co-ordinatize Steiner Systems by algebras. The examples in this chapter establishes a correspondence between all Steiner Systems of a fixed type (1, k) and a class of algebras' defined by a set of identities. Every such algebra co-ordinatizes a Steiner System of the respective type and each (t, k)-Steiner System is the underlying system of some (sometimes many) algebras in the class. The co-ordinatization is unique only for sloops, squags, and SQS-skeins (for squags and SQS-skeins it is even functorial). Except for near boolean algebras, every co-ordinatizating algebra can be obtained from a Steiner System.

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