Journal of New Theory, no.35, pp.72-90, 2021 (Peer-Reviewed Journal)
In this paper, we present a generalization of the concept of the bimultiplication algebra by defining the bimultiplication of crossed modules in associative
algebras. Using this structure, we construct the actor of a crossed module in associative algebras, and we obtain annihilators of crossed modules as the kernel of a crossed
module morphism from a crossed module to its actor. Moreover, we construct a link
between this morphism and a crossed square, two-dimensional crossed module.