Definition 1

Let $A$ be a ring, $J$ an ideal of $A$. One says that the ideal $J$ is completely secant at the point $p$ of $V(J)$ if the ideal $J_p$ of $A_p$ is generated by a completely secant sequence for $A_p$. One says that $J$ is completely secant if it is so at every point of $V(J)$.

If the ideal $J$ of $A$ is completely secant, the same is true of the ideal $S^{-1}J$ of $S^{-1}A$ for every multiplicative subset $S$ of $A$.

Every ideal generated by a completely secant sequence is completely secant. More precisely: