Segments of ordered sets
W. D. Duthie · Transactions of the American Mathematical Society · 1942
complements.A lattice in which every element has a complement is called complemented.L is modular if a¿c implies (a + b)c = a+bc for all b, c£F; distributive if (a + b)c = ac+bc for all a, b, c^L; complete if any subset of elements of L has a least upper and greatest lower bound in L. Two lattices L and L* ase isomorphic if there is a one-one mapping of their elements such that aa*, ¿h->¿>* implies a+b*-+a*+b* and aba*ö* and a*-|-è*.The set-theoretical intersection of two subsets A and B of elements of a lattice will be denoted by AC\B.a<b means a<b and a