International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 49-52, Pages 2629-2639
doi:10.1155/S0161171204309154

On the class of QS-algebras

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.