Theorems · Theorem · ring theory
TwoSidedIdeal.mem_matrix
∀ {R : Type u_1} (n : Type u_2) [inst : NonUnitalNonAssocRing R] [inst_1 : Fintype n] (I : TwoSidedIdeal R)
(M : Matrix n n R), M ∈ TwoSidedIdeal.matrix n I ↔ ∀ (i j : n), M i j ∈ I- Defined in
- Mathlib.LinearAlgebra.Matrix.Ideal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalNonAssocRingFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- NonUnitalNonAssocRingstatement and proof · cited by 354
- TwoSidedIdealstatement and proof · cited by 151
- TwoSidedIdeal.matrixstatement · cited by 10
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.