Mathlib Map

Theorems · Theorem · ring theory

Subalgebra.le_centralizer_iff

∀ {R : Type u_1} [inst : CommSemiring R] {A : Type u_2} [inst_1 : Semiring A] [inst_2 : Algebra R A]
  (S T : Subalgebra R A), S ≤ Subalgebra.centralizer R ↑T ↔ T ≤ Subalgebra.centralizer R ↑S
Defined in
Mathlib.Algebra.Algebra.Subalgebra.Centralizer
Cited by
2 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Subalgebra.centralizer_coe_iSup · cited by 0Subalgebra.centralizer_co…Subalgebra.centralizer_coe_sup · cited by 0Subalgebra.centralizer_co…Semiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringSetLike.coe · cited by 8199SetLike.coeSubalgebra · cited by 1353SubalgebraSubalgebra.centralizer · cited by 25Subalgebra.centralizerSubalgebra.le_centralizer_iffCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.