Theorems of Gelfand-Mazur type and continuity of epimorphisms from b(K)

We prove that a commutative unital Banach algebra which is a valuation ring must reduce to the field of complex numbers, which implies that every homomorphism from l∞ onto a Banach algebra is continuous. We show also that if b ϵ [b Rad B]− for some nonnilpotent element b of the radical of a commutative Banach algebra B, then the set of all primes of B cannot form a chain, and we deduce from this result that every homomorphism from b(K) onto a Banach algebra is continuous.