Let $\mathcal{A}$ be a Banach algebra and $n>1$, a fixed integer. The main objective of this paper is to talk about the commutativity of Banach algebras via its projections. Precisely, we prove that if $\mathcal{A}$ is a prime Banach algebra admitting a continuous projection $\mathcal{P}$ with image in $\mathcal{Z}(\mathcal{A})$ such that $\mathcal{P}(a^n)=a^n\text{for all}a\in \mathcal{G}$, the nonvoid open subset of $\mathcal{A}$, then $\mathcal{A}$ is commutative and $\mathcal{P}$ is the identity mapping on $\mathcal{A}$. Apart from proving some other results, as an application we prove that, a normed algebra is commutative iff the interior of its center is non-empty. Furthermore, we provide some examples to show that the assumed restrictions cannot be relaxed. Finally, we conclude our paper with a direction for further research.

Let $n\ge 1$ be a fixed integer. Within this study, we present a novel approach for discovering reversible codes over rings, leveraging the concept of $r$-glifted polynomials. This technique allows us to achieve optimal reversible codes. As we extend our methodology to the domain of DNA codes, we establish a correspondence between $4t$-bases of DNA and elements within the ring $R_{2t}=F_{4^{2t}}[u]/(u^2-1)$. By employing a variant of $r$-glifted polynomials, we successfully address the challenges of reversibility and complementarity in DNA codes over this specific ring. Moreover, we are able to generate reversible and reversible-complement DNA codes that transcend the limitations of being linear cyclic codes generated by a factor of $x^n-1$.