Geodesic
On Set Theoretically and Cohomologically Complete Intersection Ideals
Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 477-484

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DOI

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.
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 
Eghbali, Majid. On Set Theoretically and Cohomologically Complete Intersection Ideals. Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 477-484. doi: 10.4153/CMB-2014-022-7
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     title = {On {Set} {Theoretically} and {Cohomologically} {Complete} {Intersection} {Ideals}},
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     doi = {10.4153/CMB-2014-022-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-022-7/}
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