Theorems · Definition · ring theory
TwoSidedIdeal.orderIsoMatrix
{R : Type u_1} →
{n : Type u_2} →
[inst : NonAssocRing R] →
[inst_1 : Fintype n] → [Nonempty n] → [DecidableEq n] → TwoSidedIdeal R ≃o TwoSidedIdeal (Matrix n n R)Two-sided ideals in $R$ are order-isomorphic with those in $Mₙ(R)$.
See also equivMatrix.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Ideal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- OrderIsostatement · cited by 874
- NonAssocRingstatement and proof · cited by 483
- TwoSidedIdealstatement and proof · cited by 151
- TwoSidedIdeal.equivMatrixproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- TwoSidedIdeal.orderIsoMatrix_apply_ringCon_rstatement · cited by 0
- TwoSidedIdeal.orderIsoMatrix_symm_apply_ringCon_rstatement · cited by 0