An Algebra Associated to a Combinatorial Geometry
نویسندگان
چکیده
1. Preliminaries. A functor from a category of combinatorial geometries, or equivalently a category of geometric lattices, to a category of commutative algebras will be described, and some properties of this functor will be investigated. In particular, a cohomology will be associated to each point of a geometry and will be derived from the associated algebra. If (G, S) is a geometry on a set S [l , p. 2.4], then L(G), or simply L when no opportunity for confusion exists, denotes the associated geometric lattice of closed subsets of S. The rank function of L or G is denoted r. A morphism
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