  The aim of this paper is to define a homology theory for racks with finite
rank N and use it to define invariants of knots generalizing the CJKLS
2-cocycle invariants related to the invariants defined in [15]. For this
purpose, we prove that N -degenerate chains form a sub-complex of the classical
complex defining rack homology. If a rack has rack rank N = 1 then it is a
quandle and our homology theory coincides with the CKJLS homology theory [6].
Nontrivial cocycles are used to define invariants of knots and examples of
calculations for classical knots with up to 8 crossings and classical links
with up to 7 crossings are provided.
