Let be a Banach algebra. It is shown that a contractible ideal of a Banach algebra is complemented by its annihilator. Then, it is proved the existence of minimal central idempotents in a contractible Banach algebra with a nonzero character. Moreover, the notion of b-contractibility and one of its equivalent forms are introduced. Throgh an example, it is shown that b-contractibility is strictly weaker than contractibility.

Keywords: Contractible Banach algebras, Minimal idempotent

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