Semigeneralized semiderivations of semiprime rings

This article focuses on introduction the definition of semigeneralized semiderivations of semiprime rings as an additive mapping D : R → R associated with a semiderivation d : R → R and the functions h, g : R → R. If for all x, y ∈ R, then D(xy) = D(x)h(y) + g(x)d(y) = d(x)g(y) + h(x)D(y). The article divided into four sections where in the first we study and investigation some results concerning semigeneralized semiderivations of semiprime rings R where we gain R contains weakly semiprime ideal. In the second section, we determined when a weakly semiprime ideal of a semiprime rings R has an unbreakable-zero element and the third contains some results about orthogonality of semigeneralized semiderivations of semiprime rings R while the final section emphasizes on composition of a semigeneralized semiderivations.