trureturingGitHub MATHEMATICAL ATLAS

Factorization / CONCEPT

A Local-to-Global Principal-Ideal Gap

The norm-two ideal is principal after localization at every nonzero prime but is not principal globally, giving an explicit positive local-to-global defect.

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DIRECT PREREQUISITES1
DIRECT CONSEQUENCES3
PROOF DEPTH1
DOCUMENT LINKS1
THEOREM

The norm-two ideal is locally principal but globally nonprincipal

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A Norm-Two Ideal in the Minus-Five Quadratic OrderA Norm-Two Ideal in the Minus-Five Quadratic OrderA Local-to-Global Principal-Ideal GapA Local-to-Global Principal-Ideal GapDegree Zero Does Not Reconstruct Global DataDegree Zero Does NotReconstruct Global DataIdeal Identity, Principality, and Generator CoordinatesIdeal Identity, Principality,and Generator CoordinatesLocal Principality Is Blind to the Global Ideal ClassLocal Principality Is Blind tothe Global Ideal Class
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Lean sourceResearch workspace
Status
Closed
Depth
1
Layer
D5/S3
Domain
Factorization
Node ID
D5/S3/Factorization/QuadraticIdeals/NormTwoIdealLocalGlobalGap
Repository path
D5/S3/Factorization/QuadraticIdeals/NormTwoIdealLocalGlobalGap.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
Source tree
143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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