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International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 49, Pages 2629-2639
http://dx.doi.org/10.1155/S0161171204309154

On the class of QS-algebras

School of Information Environment, Tokyo Denki University, Inzai 270-1382, Japan

Received 19 September 2003

Copyright © 2004 Hindawi Publishing Corporation. 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 consider some fundamental properties of QS-algebras and show that (1) the theory of QS-algebras is logically equivalent to the theory of Abelian groups, that is, each theorem of QS-algebras is provable in the theory of Abelian groups, and conversely, each theorem of Abelian groups is provable in the theory of QS-algebras; and (2) a G-part G(X) of a QS-algebra X is a normal subgroup generated by the class of all elements of order 2 of X when it is considered as a group.