Theorems · Theorem · commutative algebra
algebraRat.charZero
∀ (R : Type u_3) [Nontrivial R] [inst : Ring R] [Algebra ℚ R], CharZero R
A nontrivial ℚ-algebra has characteristic zero.
This cannot be a (local) instance because it would immediately form a loop with the
instance DivisionRing.toRatAlgebra. It's probably easier to go the other way: prove CharZero R
and automatically receive an Algebra ℚ R instance.
- Defined in
- Mathlib.Algebra.CharP.Algebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NontrivialRingAlgebra
Around this declaration
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Nontrivialstatement and proof · cited by 2,416
- CharZerostatement · cited by 932
- CharP.charP_to_charZeroproof · cited by 11
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