Homology theories for associative algebraic structures are well established and have been studied for a long time. More recently, homology theories for selfdistributive algebraic structures motivated by knot theory, such as quandles and their relatives, have been developed and investigated. In this paper, we study associative self-distributive algebraic structures and their one-term and two-term (rack) homology groups.
Crans, Alissa, et al. “On Homology of Associative Shelves.” Journal of Homotopy & Related Structures, vol. 12, no. 3, Sept. 2017, pp. 741–763. doi:10.1007/s40062-016-0164-9.