%0 Journal Article
%T Homology of Distributive Lattices
%A Jozef H. Przytycki
%A Krzysztof K. Putyra
%J Mathematics
%D 2011
%I arXiv
%R 10.1007/s40062-012-0012-5
%X We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of its properties. The main result is a complete formula for the homology of a finite distributive lattice. We also indicate the answer for unital spindles and conjecture the general formula for semi-lattices and some skew lattices. Then we propose a generalization of a lattice as a set with a number of idempotent operations satisfying the absorption law.
%U http://arxiv.org/abs/1111.4772v1