Dedekind finite rings and a theorem of Kaplansky

摘要

A ring R is Dedekind Finite (=DF) if xy = 1 implies yx = 1 for all x, y in R. Obviously any subring of a DF ring R is DF. The object of the paper is to generalize, and give a radically new proof of a theorem of Kaplansky on group algebras that are Dedekind finite. We shall prove that all right subrings of right and left self-injective (it fact, continuous) rings are DF. [References: 16]