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Published online by Cambridge University Press: 20 November 2018
We show that the following ${{K}_{0}}$-monoid properties of ${{C}^{*}}$-algebras in the class $\Omega $ are inherited by simple unital ${{C}^{*}}$-algebras in the class $TA\Omega :$ (1) weak comparability, (2) strictly unperforated, (3) strictly cancellative.