Theorems · Theorem · ring theory
IsAzumaya.matrix
∀ (R : Type u_1) (n : Type u_2) [inst : CommSemiring R] [inst_1 : Fintype n] [inst_2 : DecidableEq n] [Nonempty n], IsAzumaya R (Matrix n n R)
A nontrivial matrix ring over R is an Azumaya algebra over R.
- Defined in
- Mathlib.Algebra.Azumaya.Matrix
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- DFunLike.congr_funproof · cited by 288
- Function.bijective_iff_has_inverseproof · cited by 50
- IsAzumayastatement · cited by 4
- AlgHom.mulLeftRightMatrix_invproof · cited by 3
- AlgHom.mulLeftRightMatrix.comp_invproof · cited by 1
- AlgHom.mulLeftRightMatrix.inv_compproof · cited by 1
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