Depth of an ideal: Difference between revisions
(New page: ==Definition== Let <math>R</math> be a commutative unital ring and <math>I</math> be an ideal inside <math>R</math>. The '''depth''' of <math>I</math> is the length of a maximal [...) |
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Latest revision as of 16:19, 12 May 2008
Definition
Let be a commutative unital ring and be an ideal inside . The depth of is the length of a maximal regular sequence in . A regular sequence is a sequence of elements where each element is not a zero divisor in the ideal spanned by the preceding elements.
A related notion is depth of an ideal on a module, where we replace zero divisor by zero divisor on the module.