Prime ideals and automatic continuity problems for Banach algebras

Conditions are given for Banach algebras $\text{U}$ and commutative Banach algebras $\text{B}$ which insure that every homomorphism v from $\text{U}$ into $\text{B}$ is continuous. Similar results are obtained for derivations which either map the algebra $\text{U}$ into itself or map the algebra into a suitable $\text{U}$-module.