Primary decomposition of general graded structures

In this paper we discuss the primary decomposition in the case of general graded modules – moduloids, a generalization of already done work for general graded rings – anneids. These structures, introduced by Marc Krasner are more general than graded structures of Bourbaki since they do not require the associativity nor the commutativity nor the unitarity in the set of grades. After proving the existence and uniqueness of primary decomposition of moduloids, we breafly turn our attention to Krull's Theorem and to the existence of the primary decomposition of Krasner–Vuković paragraded rings.