A lattice is a mathematical construction built on the notion of a group. First, we review some basic terms. Then we discuss lattices.

For a set *S*, a relation *R* is any subset of *S* × *S*. For convenience, if (*a, b*) ∊ *R*, we write *aRb*.

The following definitions describe properties of relations.

A relation**Definition 30–1.***R*defined over a set*S*is*reflexive*if*aRa*for all*a*∊*S*.A relation**Definition 30–2.***R*defined over a set*S*is*antisymmetric*if*aRb*and*bRa ...*

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