International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 78981, 8 pages
Decompositions of a -algebra
Department of Mathematics, Andhra University, Visakhapatnam 530 003, India
Received 12 April 2005; Revised 12 December 2005; Accepted 18 December 2005
Copyright © 2006 G. C. Rao and P. Sundarayya. 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 prove that if is a -algebra, then for each , is itself a -algebra and is isomorphic to the quotient algebra of where . If is -algebra with , we prove that for every , the centre of , is isomorphic to and that if is isomorphic , then there exists such that is isomorphic and is isomorphic to . Using this decomposition theorem, we prove that if with , then is isomorphic to if and only if there exists an isomorphism on such that .