`International Journal of Mathematics and Mathematical SciencesVolume 2006 (2006), Article ID 78981, 8 pagesdoi:10.1155/IJMMS/2006/78981`

# G. C. Rao and P. Sundarayya

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.

#### Abstract

We prove that if A is a C-algebra, then for each aA, Aa={xA/xa} is itself a C-algebra and is isomorphic to the quotient algebra A/θa of A where θa={(x,y)A×A/ax=ay}. If A is C-algebra with T, we prove that for every aB(A), the centre of A, A is isomorphic to Aa×Aa and that if A is isomorphic A1×A2, then there exists aB(A) such that A1 is isomorphic Aa and A2 is isomorphic to Aa. Using this decomposition theorem, we prove that if a,bB(A) with ab=F, then Aa is isomorphic to Ab if and only if there exists an isomorphism φ on A such that φ(a)=b.