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Let R be an associative ring. A *- semimultiplier is an additive map F : R = R such that F(xy) = F(x)g(y8) = g(x*)F(y) where g is some additive map and F(g(x)) = g(F(x)) for all x 2 R . We make extensive use of functional identities defined in prime ring R of the forms xE1(y) + yE2(x) = 0 or xE1(y) + yE2(x) 2 Z(R) = C where E1, E2 are any arbitrary functions on the prime ring R and Z(R), C are the center and the extended centroid of R respectively. We have proved that in a prime ring R under some additional conditions, a 8 - semimultiplier F : R = R is a map given by F(x) = x + (x), where * 2 C and : R = C. We have also shown that a prime ring admitting the *-semimultiplier satisfies S4, the standard identity of degree 4 under some suitable conditions. Further, some other important results are also incorporated. [ABSTRACT FROM AUTHOR]

We present an historical account of the study of derivations, generalized deriva-tions, n-derivations, generalized n-derivation and other kinds of derivations in near-rings, based on the work of several authors. Moreover, recent results on semigroup ideals and generalized n-derivations on these topics have been discussed in details. Examples of various notions have also been included. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized n-derivation in near-ring N and investigate several identities involving generalized n-derivations of a prime near-ring N which force N to be a commutative ring. Finally some more related results are also obtained. [ABSTRACT FROM AUTHOR]