Adjunction of unity and invertible elements in uniformly locally a-convex algebras

We show by a counter example that the adjunction of unity is not always possible for the class of uniformly locallyA-convex algebras contrary to Cochran's affirmation and we characterize uniformly locallyA-convex algebras for which this adjunction is possible. We also exhibit examples of complete uniformly locallyA-convex algebras which do not satify properties of Banach algebras.