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

Universal decomposition algebras and the classification of 2-generated non-primitive axial algebras of Jordan type