In this paper for a locally compact group $G$ and a decreasing sequence of weight functions $\{\omega_n\}$ on it with $\omega_n> 1$ ($n\in {\Bbb N}$), we show that Fr\'echet algebra $\cap_{n\in {\Bbb N}}L^\infty(G,\omega^{-1}_n)$ is projective if and only if $G$ is finite and Fr\'echet algebra $\cap_{n\in {\Bbb N}}C_0(G,\omega^{-1}_n)$ is projective (injective) if and only if $G$ is compact (finite). Similar result will be shown for Fr\'echet algebra $\cap_{n\in {\Bbb N}}L_0^\infty(G,\omega^{-1}_n)$.
