Irreducible Unital Right Alternative Bimodules

Right alternative bimodules over the matrix algebra M2(F) are investigated. It is shown that, contrary to the Jordan and alternative cases, there are infinitely many irreducible right alternative bimodules over this algebra. The irreducible unital bimodules up to dimension 6 are classified. An example of an indecomposable bimodule that is not irreducible is also constructed.