Theorems · Theorem · commutative algebra
Subring.closure_le_centralizer_centralizer
∀ {R : Type u_1} [inst : Ring R] (s : Set R), Subring.closure s ≤ Subring.centralizer ↑(Subring.centralizer s)- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- SetLike.coestatement · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Subringstatement · cited by 602
- Subring.closurestatement · cited by 78
- Subring.closure_leproof · cited by 14
- Set.subset_centralizer_centralizerproof · cited by 13
- Subring.centralizerstatement · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Subring.isMulCommutative_closureproof · cited by 0