On the class of QS‐algebras
Michiro Kondo · International Journal of Mathematics and Mathematical Sciences · 2004
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.