Remark on the Unital Quantale Q[e]

In this paper, we investigate some properties of the unital quantale Q[e], in terms of the quantic quotients of Q[e] we study the extensions of quantic nuclei of Q to Q[e] and prove that for any non-trivial quantale $\textbf{Q}$, Q[e] is not simple. Also, we give some applications for the unital quantale Q[e].