  The isomorphism of Karoubi-Villamayor K-groups with smooth K-groups for
monoid algebras over quasi stable locally convex algebras is established and we
prove that the Quillen K- groups are isomorphic to smooth K-groups for monoid
algebras over quasi-stable Frechet algebras having a properly uniformly bounded
approximate unit. Based on these results the K-regularity property for
quasi-stable Frechet algebras having a properly uniformly bounded approximate
unit is established.
