Theorems · Definition · ring theory
TwoSidedIdeal.matrix
{R : Type u_1} →
(n : Type u_2) →
[inst : NonUnitalNonAssocRing R] → [inst_1 : Fintype n] → TwoSidedIdeal R → TwoSidedIdeal (Matrix n n R)The two-sided ideal of matrices with entries in I ≤ R.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Ideal
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 61 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.
Cites6
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 · cited by 4,303
- NonUnitalNonAssocRingstatement and proof · cited by 354
- TwoSidedIdealstatement and proof · cited by 151
- TwoSidedIdeal.ringConproof · cited by 40
- RingCon.matrixproof · cited by 10
Cited by11
Results whose statement or proof uses this declaration.
- TwoSidedIdeal.equivMatrixproof · cited by 4
- TwoSidedIdeal.matrix_botstatement and proof · cited by 1
- TwoSidedIdeal.matrix_monotonestatement and proof · cited by 1
- TwoSidedIdeal.asIdeal_matrixstatement · cited by 1
- TwoSidedIdeal.jacobson_matrixstatement and proof · cited by 1
- TwoSidedIdeal.matrix_jacobson_botstatement · cited by 0
- TwoSidedIdeal.matrix_ringConstatement and proof · cited by 0
- TwoSidedIdeal.matrix_strictMono_of_nonemptystatement · cited by 0
- TwoSidedIdeal.matrix_topstatement and proof · cited by 0
- TwoSidedIdeal.equivMatrix_applystatement · cited by 0
- TwoSidedIdeal.mem_matrixstatement · cited by 0