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The ``extended'' BF-Yang-Mills theory in 3 dimensions, which contains aminimally coupled scalar field, is shown to be ultraviolet finite. It obeys atrivial Callan-Symanzik equation, with all beta-functions and anomalousdimensions vanishing. The proof is based on an anomaly-free trace identityvalid to all orders of perturbation theory.Comment: 11 pages, Late

Exact scale invarianmce of the BF-Yang-Mills theory in three dimensions