Let F be a class of entire functions represented by Dirichlet series with complex frequencies ∑ ake hλ k ,zi for which (|λ k |/e)|λ k | k!|ak| is bounded. Then F is proved to be a commutative Banach algebra with identity and it fails to become a division algebra. F is also proved to be a total set. Conditions for the existence of inverse, topological zero divisor and continuous linear functional for any element belonging to F have also been established.