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It is known that for an IP${^\star}$ set $A$ in $\mathbb{N}$ and a sequence$< x_{n}>_{n=1}^{\infty}$ there exists a sum subsystem $<y_{n}>_{n=1}^{\infty}$ of $< x_{n}>_{n=1}^{\infty}$ such that  $FS(< y_n>_{n=1}^\infty)\cup FP(< y_n>_{n=1}^\infty)\subseteq A$. Similartypes of results also have been proved for central* sets where the sequenceshave been taken from the class of minimal sequences. In this present work wewill prove some analogues results for C$^{\star}$-sets for a more general classof sequences.

Additive and multiplicative structure of c$^{\star}$-sets