Abstract
The isomorphism of Karoubi–Villamayor K-groups with smooth K-groups for monoid algebras over quasi-stable locally convex algebras is established. We prove that the Quillen K-groups are isomorphic to smooth K-groups for monoid algebras over quasi-stable Fr $$\acute{\mathrm{e}}$$ chet algebras having a properly uniformly bounded approximate unit and not necessarily m-convex. Based on these results the K-regularity property for quasi-stable Fr $$\acute{\mathrm{e}}$$ chet algebras having a properly uniformly bounded approximate unit is established.
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