The notion of reverse derivation is studied and some properties are obtained. It is shown that in the class of semiprime rings, this notion coincides with the usual derivation when it maps a semiprime ring into its center. However, we provide some examples to show that it is not the case in general. Also it is shown that non-commutative prime rings do not admit a non-trivial skew commuting derivation. Mathematics Subject Classification: 16A70, 16N60, 16W25Keywords: Prime ring, semiprime ring, anticommutative, derivation, reverse derivation, skew commuting map PreliminariesThroughout, R denotes a ring with center Z(R). We write [x, y] for xy − yx. Recall that a ring R is called prime if aRb = 0 implies a = 0 or b = 0; and

Abstract. In this note we investigate some properties of a-derivations on prime and semiprime rings. We establish some identities for a commuting a-derivation d on a semiprime ring R and show that d maps R into its center and obtain some well-known results as a consequence. We also generalize Posner's theorem on the composition of derivations for a-derivations and as an application resolve a functional equation of automorphisms on certain prime rings.

We identify some strong commutativity-preserving maps on semiprime rings. Among other results, we prove the following. (i) A centralizing homomorphism f of a semiprime ring R onto itself is strong commutativity preserving. (ii) A centralizing antihomomorphism f of a 2-torsion-free semiprime ring R onto itself is strong commutativity preserving

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The set of all endomorphisms of an algebraic structure with composition of functions as operation is a rich source of semigroups, which has only rarely been dipped into (see [2]). Here we make a start by considering endomorphisms of Clifford semigroups, relating them to the homomorphisms and endomorphisms of the underlying groups.