Rings on Vector Abelian Groups

A multiplication on an Abelian group G is a homomorphism μ: ⊗ → G. An with it called ring the R. A. Beaumont and D. Lawver have formulated problem of studying semisimple groups. said to be if there exists associative it. Semisimple groups are described in class vector nonmeasurable It also shown that set I nonmeasurable, $$ G=\coprod_{i\in I}{A}_i reduced group, μ G, then determined by its restriction sum {\displaystyle \begin{array}{c}\oplus \\ {}i\in I\end{array}}{A}_i this statement incorrect measurable or not reduced.