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On Set Theoretically and Cohomologically Complete Intersection Ideals

Published online by Cambridge University Press:  20 November 2018

Majid Eghbali
Majid Eghbali*
Affiliation:
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran-Iran e-mail: m.eghbali@yahoo.com
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Abstract

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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.

Keywords

13D4513C14set-theoretically and cohomologically complete intersection idealsanalytic spreadmonomialsformal gradedepth of powers of ideals
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 3 , 01 September 2014 , pp. 477 - 484
Copyright
Copyright © Canadian Mathematical Society 2014

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