Semisimple Rings On Completely Decomposable Abelian Groups

摘要

An Abelian group is said to be semisimple if it is the additive group of some semisimple associative ring. The problem of describing semisimple groups was formulated by Beaumont and Lawver; later this problem was reduced to the case of reduced groups. In this paper, we describe semisimple groups in the class of countable completely decomposable groups.