On set theoretically and cohomologically complete intersection ideals

Majid eghbali

doi:10.4153/cmb-2014-022-7

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arXiv · 1211.5942

On set theoretically and cohomologically complete intersection ideals

Majid eghbali

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Abstract

Let $(R,\fm)$ be a local ring and $\fa$ be an ideal of $R$. The inequalities $$\begin{array}{ll} \ \Ht(\fa) \leq \cd(\fa,R) \leq \ara(\fa) \leq l(\fa) \leq μ(\fa) \end{array}$$ are known. It is an interesting and long-standing problem to find out the cases giving equality. Thanks to the formal grade we give conditions in which the above inequalities become equalities.

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Majid eghbali. 2014-04-03. On set theoretically and cohomologically complete intersection ideals. https://doi.org/10.4153/cmb-2014-022-7

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