Theorems · Theorem · commutative algebra
expChar_of_injective_algebraMap
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A],
Function.Injective ⇑(algebraMap R A) → ∀ (q : ℕ) [ExpChar R q], ExpChar A qIf the algebra map R →+* A is injective then A has the same exponential characteristic
as R.
- Defined in
- Mathlib.Algebra.CharP.Algebra
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- ExpCharstatement and proof · cited by 276
- expChar_of_injective_ringHomproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparableproof · cited by 4
- IsPurelyInseparable.tower_topproof · cited by 3
- exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_powproof · cited by 2
- minpoly.natSepDegree_eq_one_iff_eq_X_sub_C_powproof · cited by 1
- LinearIndependent.map_of_isPurelyInseparable_of_isSeparableproof · cited by 1
- perfectField_of_perfectClosure_eq_botproof · cited by 1
- IsPurelyInseparable.transproof · cited by 1
- Field.span_map_pow_expChar_pow_eq_top_of_isSeparableproof · cited by 0