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Thus the propositions of any deductive system (e.g., lattice theory or group theory
) form a poset when partially ordered by the implication relation. Mathematics is
concerned with many other familiar partial orderings, such as the relation x < y of
symmetric laws, considered as postulates used to define the abstract concept of a
poset. Conversely, a lattice can be defined as an algebraic system, or algebra,
having two commutative, associative, idempotent, and contractive operations.
The most general finite distributive lattice may be constructed by a simple
generalization of Skolem's theorem. Namely, L is assumed to be any finite
distributive lattice, and A is assumed to be the set of all properly join-irreducible
elements of L; ...
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The New Encyclopaedia Britannica (Encyclopaedia)User Review - Not Available - Book Verdict
For virtually all its 238 years,Britannica has ruled the shelves as a peerless general encyclopedia. Reviewers have consistently given it high marks for most of the 12 criteria identified inKister's ... Read full review