On Set Theoretically and Cohomologically Complete Intersection Ideals

Eghbali, Majid

Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 477-484

Résumé

Let $\left( R,\,\mathfrak{m} \right)$ be a local ring and $\mathfrak{a}$ be an ideal of $R$ . The inequalities $$\text{ht}\left( \mathfrak{a} \right)\,\le \,\text{cd}\left( \mathfrak{a},\,R \right)\,\le \,\text{ara}\left( \mathfrak{a} \right)\,\le \,l\left( \mathfrak{a} \right)\,\le \,\mu \left( \mathfrak{a} \right)$$ are known. It is an interesting and long-standing problem to determine the cases giving equality. Thanks to the formal grade we give conditions in which the above inequalities become equalities.

Détail

DOI : 10.4153/CMB-2014-022-7

Mots-clés : 13D45, 13C14, set-theoretically and cohomologically complete intersection ideals, analytic spread, monomials, formal grade, depth of powers of ideals

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