  Decomposition algebras and axial decomposition algebras are classes of
commutative nonassociative algebras which are generalizations of axial
algebras. The classes decomposition algebras, axial decomposition al;gebras and
non-primitive axial algebras also have univesal algebras. Furthermore, by using
the existence of a universal algebra, 2-generated non-primitive axial algebras
of Jordan type is classified.
