Theorems · Theorem · commutative algebra
is_noetherian_subring_closure
∀ {R : Type u} [inst : CommRing R] (s : Set R), s.Finite → IsNoetherianRing ↥(Subring.closure s)- Defined in
- Mathlib.RingTheory.Adjoin.FG
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Set.Finitestatement and proof · cited by 1,814
- Subringstatement · cited by 602
- IsNoetherianRingstatement and proof · cited by 268
- Subring.closurestatement and proof · cited by 78
- subalgebraOfSubringproof · cited by 5
- Subalgebra.fg_defproof · cited by 3
- isNoetherianRing_of_fgproof · cited by 2
- Algebra.adjoin_intproof · cited by 2
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