“…Thenceforth, diverse works have been published considering different types of associative and non-associative algebras. Among them we can mention [9,11,12,8,13,10,14,3]. In order to further develop the study of additivity of maps, the researches incorporated two new product into the theory, presented by Brešar and Fošner in [2,15], where the definition is as follows: for X, Y ∈ R , where R is a * −ring, we denote by X • Y = XY + Y X * and [X, Y ] * = XY − Y X * the * -Jordan product and the * -Lie product, respectively.…”