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On Set Theoretically and Cohomologically Complete Intersection Ideals

  Published:2014-04-28
 Printed: Sep 2014
  • Majid Eghbali,
    School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran-Iran
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Abstract

Let $(R,\mathfrak m)$ be a local ring and $\mathfrak a$ be an ideal of $R$. The inequalities \[ \operatorname{ht}(\mathfrak a) \leq \operatorname{cd}(\mathfrak a,R) \leq \operatorname{ara}(\mathfrak a) \leq l(\mathfrak a) \leq \mu(\mathfrak a) \] 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.
Keywords: set-theoretically and cohomologically complete intersection ideals, analytic spread, monomials, formal grade, depth of powers of ideals set-theoretically and cohomologically complete intersection ideals, analytic spread, monomials, formal grade, depth of powers of ideals
MSC Classifications: 13D45, 13C14 show english descriptions Local cohomology [See also 14B15]
Cohen-Macaulay modules [See also 13H10]
13D45 - Local cohomology [See also 14B15]
13C14 - Cohen-Macaulay modules [See also 13H10]
 

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