ABSTRACT
We prove that if R is a semiartinian unit-regular ring, then the group K 0(R) is free. When R satisfies the restricted comparability axiom (see below for the definition), in particular when all Loewy factors R/Soc α (R) are prime for α less than the Loewy length of R, we show that K 0(R) is a suitable lexicographic direct sum of free abelian groups each with the pointwise ordering.
