Aleph-Nought-continuous regular rings

Let R be a right א0-continuous regular ring. We show that there exists a two-sided ideal I of R such that R I is a directly finite, right א0-continuous regular ring and each directly finite factor ring of R is a factor ring of R I. By using this, we extend to arbitrary right א0-continuous regular rings some of the results obtained by Goodearl for directly finite, right א0-mcontinuous regular rings. © 1987.