2 THE PRIMITIVE IDEAL SPACE OF THE C*-ALGEBRA OF THE AFFINE SEMIGROUP OF ALGEBRAIC INTEGERS
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Bibliographic record
Abstract
Abstract The purpose of this paper is to give a complete description of the primitive ideal space of the C*-algebra [ R ] associated to the ring of integers R in a number field K in the recent paper [ 5 ]. As explained in [ 5 ], [ R ] can be realized as the Toeplitz C*-algebra of the affine semigroup R ⋊ R × over R and as a full corner of a crossed product C 0 ( ) ⋊ K ⋊ K *, where is a certain adelic space. Therefore Prim( [ R ]) is homeomorphic to the primitive ideal space of this crossed product. Using a recent result of Sierakowski together with the fact that every quasi-orbit for the action of K ⋊ K * on contains at least one point with trivial stabilizer we show that Prim( [ R ]) is homeomorphic to the quasi-orbit space for the action of K ⋊ K * on , which in turn may be identified with the power set of the set of prime ideals of R equipped with the power-cofinite topology.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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