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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 368527, 13 pages
Research Article

On the Homology Theory of Operator Algebras

Department of Math, Faculty of Science, Aswan University, Aswan 81528, Egypt

Received 31 May 2012; Accepted 22 October 2012

Academic Editor: Nistor Victor

Copyright © 2012 Alaa Hassan Noreldeen. 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.


We investigate the cyclic homology and free resolution effect of a commutative unital Banach algebra. Using the free resolution operator, we define the relative cyclic homology of commutative Banach algebras. Lemmas and theorems of this investigation are studied and proved. Finally, the relation between cyclic homology and relative cyclic homology of Banach algebra is deduced.