SWhat changed
Ascending-chain/finite-generation conditions organize ideal decomposition: ideals in the specified commutative rings can be expressed as finite intersections of primary ideals, with scoped structural uniqueness statements.
Scientific scope
Ascending-chain/finite-generation conditions organize ideal decomposition: ideals in the specified commutative rings can be expressed as finite intersections of primary ideals, with scoped structural uniqueness statements. The finiteness condition is essential. Primary components need not be unique, and a primary ideal need not be a power of a prime. This does not assert decomposition in arbitrary rings.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Emmy Noether · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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