Theorems · Theorem · ring theory
Algebra.rank_adjoin_le
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] (s : Set S),
Module.rank R ↥(Algebra.adjoin R s) ≤ max (Cardinal.mk ↑s) Cardinal.aleph0- Defined in
- Mathlib.LinearAlgebra.FreeAlgebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Set.Elemstatement and proof · cited by 7,166
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- Nontrivialproof · cited by 2,416
- Subalgebrastatement and proof · cited by 1,353
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftproof · cited by 583
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