Abstract
Let be a ring homomorphism and I be an ideal of B. The amalgamated algebra of A and B along I with respect to f is the subring of A × B given by
In this paper, we give a complete description of derivations over . The obtained results cover some recent results over duplication of a ring along an ideal. Furthermore, it’s shown that if A is a prime ring with 1 and d is a nonzero derivation of
such that, for each
d(x) = 0 or d(x) is invertible in
then A is a division ring and
is identified to
where D is a division ring, char(D) = 2,
and
for some