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Let $F$ be a class of entire functions represented by Dirichlet series with complex frequencies $\sum a_k{\mathrm{e}}^{\langle {\lambda }^k,z\rangle }$ for which $\left(\right|{\lambda }^k{|/\mathrm{e})}^{|{\lambda }^k|}k!\left|a_k\right|$ 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.