International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 49, Pages 2629-2639
On the class of -algebras
School of Information Environment, Tokyo Denki University, Inzai 270-1382, Japan
Received 19 September 2003
Copyright © 2004 Michiro Kondo. 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 consider some fundamental properties of -algebras and show that (1) the theory of -algebras is logically equivalent to the theory of Abelian groups, that is, each theorem of -algebras is provable in the theory of Abelian groups, and conversely, each theorem of Abelian groups is provable in the theory of -algebras; and (2) a -part of a -algebra is a normal subgroup generated by the class of all elements of order 2 of when it is considered as a group.