SUM-REPRESENTATIONS OF FINITE LATTICES
Joanna Grygiel · 2001
Every flnite lattice can be represented as a Wronski sum of its sum-irreducible in- tervals. We prove that the set of terms describing all possible sum-representations of a given lattice K determines uniquely this lattice. Let A = hA;•Ai and B = hB;•Bi be flnite lattices such that A B is a fllter in A and an ideal in B andA =A\B =•B =A\B. Then A ' B = hA ( B;•i, whereis the transitive closure ofA ( •B, is a flnite lattice called a sum of A and B. This sum operation was introduced by A. Wronski in (8). It is obvious that this operation is neither commutative nor associative. However, it has the following properties: