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Theorems · Definition · ring theory

RingCon.ofMatrix

{R : Type u_1} →
  {n : Type u_2} →
    [inst : NonUnitalNonAssocSemiring R] → [inst_1 : Fintype n] → [DecidableEq n] → RingCon (Matrix n n R) → RingCon R

The congruence relation induced by c on single i j.

Defined in
Mathlib.LinearAlgebra.Matrix.Ideal
Cited by
6 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonUnitalNonAssocSemiringFintypeDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

TwoSidedIdeal.equivMatrix · cited by 4TwoSidedIdeal.equivMatrixRingCon.coe_ofMatrix_eq_relationMap · cited by 1RingCon.coe_ofMatrix_eq_r…TwoSidedIdeal.equivMatrix_symm_apply_ringCon · cited by 1TwoSidedIdeal.equivMatrix…RingCon.ofMatrix_matrix · cited by 0RingCon.ofMatrix_matrixRingCon.ofMatrix_rel · cited by 0RingCon.ofMatrix_relRingCon.ofMatrix_rel' · cited by 0RingCon.ofMatrix_rel'RingCon.matrix_ofMatrix · cited by 0RingCon.matrix_ofMatrixDFunLike.coe · cited by 62936DFunLike.coeFintype · cited by 7736FintypeMatrix · cited by 4303MatrixNonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringRingCon · cited by 219RingConMatrix.single · cited by 129Matrix.singleRingCon.ofMatrixCITED BYCITES

Cites6

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

Cited by7

Results whose statement or proof uses this declaration.