Theorems · Theorem · ring theory
Commute.lie_eq
∀ {R : Type u} [inst : NonUnitalNonAssocRing R] {x y : R}, Commute x y → ⁅x, y⁆ = 0- Defined in
- Mathlib.Algebra.Ring.Commute
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- NonUnitalNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bracket.bracketstatement · cited by 642
- Commutestatement and proof · cited by 639
- NonUnitalNonAssocRingstatement and proof · cited by 354
- sub_eq_zero_of_eqproof · cited by 154
Cited by3
Results whose statement or proof uses this declaration.
- LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithfulproof · cited by 1
- two_nsmul_lie_lmul_lmul_add_add_eq_zeroproof · cited by 0
- two_nsmul_lie_lmul_lmul_add_eq_lie_lmul_lmul_addproof · cited by 0