IN the theory of infinite abelian groups, the concepts of torsion-free groups and divisible groups are well known. We know that there exists, up to isomorphism, one and only one abelian group which is both torsion-fre...IN the theory of infinite abelian groups, the concepts of torsion-free groups and divisible groups are well known. We know that there exists, up to isomorphism, one and only one abelian group which is both torsion-free and divisible at the same time. This is the additive group Q of the rational numbers. Q plays an important role in the study of infinite-abelian groups. The theory of infinite-dirnensional modules over a finite-dimensional algebra runs similarly to the theory of infinite abelian groups but there are also some substantial differences.展开更多
文摘IN the theory of infinite abelian groups, the concepts of torsion-free groups and divisible groups are well known. We know that there exists, up to isomorphism, one and only one abelian group which is both torsion-free and divisible at the same time. This is the additive group Q of the rational numbers. Q plays an important role in the study of infinite-abelian groups. The theory of infinite-dirnensional modules over a finite-dimensional algebra runs similarly to the theory of infinite abelian groups but there are also some substantial differences.
