Int. Journal of Math. Analysis, Vol. 7, 2013, no. 59, 2931 - 2939 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2013.39228 On Villena’s Theorem of Automatic Continuity of Essentially Defined Derivations on Semisimple Banach Algebras Amir A. Mohammed a and Suham M. Ali b a Department of Mathematics, College of Education University of Mousul, Mousul, Iraq amirabdulillah@yahoo.com b Department of Mathematics, College of Sciences University of Kirkuk, Kirkuk, Iraq sumoal_73@yahoo.com Copyright © 2013 Amir A. Mohammed and Suham M. Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Following Villena in [4], we prove that every partially defined -c-derivation on a semisimple complex Banach algebra whose domain is a (non necessarily closed) essential ideal is closable. In particular, we show that every -c-derivation defined on any nonzero ideal of a prime C * - algebra is continuous. Keywords: automatic continuity, - derivation, ultraprimness , sliding hump sequence 0. Introduction Throughout the paper,  is a semisimple Banach algebra over a complex field and   a continuous linear mapping. If  is the identity map and if