Overall statement or summary

An additive mapping F : R to R is called a generalized derivation on R if there exists a derivation d: R to R such that F(xy) = xF(y) + d(x)y holds for every x, y in R. F is called a generalized (alpha,beta)-derivation on R if there exists an (alpha,beta)-derivation d: R to R such that the equation F(xy) = F(x)alpha(y)+beta(x)d(y) holds for for every x, y in R. The authors investigated the commutativity of a prime ring R and they studied identities involving generalized (alpha, beta)-derivation F associated with (alpha, beta)-derivation d, for which R is a prime ring with involution *, and F and d satisfy certain differential identities on the left ideals of R in what follows: (i) F(x)ox in Z(R), (ii)[F(x), F(y)]-F[x; y] in Z(R), (iii) F(x)oF(y)-F(xoy) in Z(R), (iv) F[x, y]+[F(x),y]- [F(x), F(y)] in Z(R), (v) F(x o y) - [x, y] in Z(R), (vi) [F(x), F(y)] - xoy in Z(R), (vii)[F(x),G(y)] - [x, y] in Z(R), (viii) [F(x), x] - [x,G(x)] in Z(R) and F(x) ox - x oG(x) in Z(R) for every x, y in some appropriate subset of R.

Strengths

Weaknesses

1. Study on semiprime rings is better than prime ring where every prime rings is semiprime rings but then the converse is not true.
2. Their conditions were just replacing derivation by generalized derivation which were not recent than previous studies. 3.Provide some examples of paper makes the results more clearly for the readers.

Major points

1. The authors presented some recent results of non commutative prime ring, and they modify it to become a commutative prime ring.

2. The authors studied a 2-torsion free -prime ring R and the mappings alpha, beta be automorphisms on R. If R admits a generalized (alpha, beta)-derivation F to satisfy some conditions then the -prime ring modify to be commutative prime ring.

3. The authors supplied chronological development about their subject.

Minor points

1. The authors wrote two remarks related to other authors. Most of references in the paper are recent and are related to the subject of paper..
2. Most of references of paper were recent and related to the subject of paper.