Representations of algebras satisfying a train identity of degree 2 and exponent 3

In this paper, we are interested in the study of representations of the algebras A satisfying the equation (a3)2 = ω(a3)a3, for all a in A. We give a characterization of these representations. We also give the condition under which the A-module is associative. When the Peirce component A1/2= 0, we give examples of sub A-modules. We show that the irreducible A-submodules are not necessarily of dimension 1.