Regular Sequence On A Module

Depends on

• Annihilators, torsion elements and the torsion subset of a module
• Quotient module $M/N$ with scalar multiplication on additive cosets

Used by

• Depth with respect to an ideal Definition
• A Cohen--Macaulay ring with zero divisors Example
• A non-Cohen--Macaulay local quotient Example
• A parameter sequence regular in a hypersurface Example
• Empty And Unit Koszul Boundaries Example
• Nonpermutable Regular Sequence Example
• Three sharp Depth Lemma inequalities Example
• A flat local map splits regular sequences into base and fibre parts Lemma
• A maximal regular sequence stops at an associated prime Lemma
• A polynomial variable increases depth by one Lemma
• Associated graded algebra of an ideal generated by a regular sequence Lemma
• auslander buchsbaum base case free module Lemma
• Completion preserves regular sequences Lemma
• Coprime positive-degree plane forms form a regular sequence Lemma
• Depth at a prime is bounded by local support dimension Lemma
• Depth drops by one after quotienting by a regular element Lemma
• Hilbert series and eventual Hilbert value of a two-form plane complete intersection Lemma
• Local Koszul Acyclicity Inductive Converse Lemma
• Local Koszul H One Detects First Regularity Failure Lemma
• Maximal regular sequences have a common Ext length Lemma
• Polynomial diagonal differences form a regular sequence Lemma
• Positive Powers Of A Regular Sequence Remain Regular Lemma
• Reflection basic invariants form a regular sequence Lemma
• Regular One Element Koszul Acyclicity Lemma
• Regular Sequence First Element Boundary Lemma
• Regular Sequence Permutation Adjacent Swap Lemma
• Regular Sequence Tail On Quotient Lemma
• The first nonzero Ext shifts across a regular element Lemma
• The first-layer relations of a closed MOY resolution form a regular sequence Lemma
• Chevalley–Eilenberg cohomology computes Ext of the trivial module Proposition
• Localisation And Faithfully Flat Base Change Of Regular Sequences Theorem
• regular local rings are domains and cohen macaulay Theorem
• Regular Sequences Give Acyclic Koszul Complexes Theorem
• Two coprime projective plane forms meet in total length equal to their degree product Theorem

Dependency tree · two levels

7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• The Stacks Project, Koszul complexes and regular sequences (standard reference, not scraped)