Transfert de la Notion de $C$-anneaux aux Produits Fibres

Othman Echi

Abstract: Let $T$ be a domain and $M$ a maximal ideal of $T$. Let $\varphi: T\to K$ be the canonical surjection where $K=T/M$. We consider the ring $R=\varphi^{-1}(D)$, where $D$ is a subring of $K$ with quotient field $k$. It is proved here that if $T$ and $D$ are $C$-rings [8] and $K$ is algebraic over $k$, then $R$ is also a $C$-ring. Other results concerning $C$-rings are also given.

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