ConceptDynamics / CONCEPT
Ideal Recovery Does Not Imply Principality
Exact recovery of an ideal does not supply a global generator. A concrete nonprincipal prime ideal is contrasted with principal-ideal rings and the degenerate zero and unit ideals.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH3
DOCUMENT LINKS1
A uniquely identified prime ideal can be nonprincipal
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
None recorded in this release.
RELATED KNOWLEDGE
Structural connections
- A Local-to-Global Principal-Ideal Gapstructural-affinity · Closed
- Degree Zero Does Not Reconstruct Global Datastructural-affinity · Closed
- Finite-Valuation Portrait Object Layerstructural-affinity · Closed
- Fractional-Ideal Prime-Valuation Faithfulnessstructural-affinity · Closed
- Ideal Identity, Principality, and Generator Coordinatesstructural-affinity · Closed
- Local Principality Is Blind to the Global Ideal Classstructural-affinity · Closed
- Principal Classes and Faithful Prime Countsstructural-affinity · Closed
- Three Completion Tasksstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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