A homology theory for a special family of semi-groups

In this paper, we construct a new homology theory for semi-groups satisfying the right self-distributivity axiom or the idempotency axiom. Next, we consider the geometric realization corresponding to the homology theory. We continue with the comparison of this homology theory with one-term and two-term (rack) homology theories of self-distributive algebraic structures. Finally, we propose connections between the homology theory and knot theory via Temperley–Lieb algebras.