Theorems · Theorem · commutative algebra
expChar_pow_pos
∀ (R : Type u_1) [inst : AddMonoidWithOne R] (q : ℕ) [ExpChar R q] (n : ℕ), 0 < q ^ n
Any power of the exponential characteristic is positive.
- Defined in
- Mathlib.Algebra.CharP.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext
- Assumes
- AddMonoidWithOneExpChar
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidWithOnestatement and proof · cited by 313
- ExpCharstatement and proof · cited by 276
- expChar_posproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- minpoly.natSepDegree_eq_one_iff_pow_memproof · cited by 4
- IsPurelyInseparable.elemExponent_le_of_pow_memproof · cited by 3
- Irreducible.natSepDegree_eq_one_iff_of_monic'proof · cited by 3
- Polynomial.rootMultiplicity_expand_powproof · cited by 2
- LinearIndependent.map_of_isPurelyInseparable_of_isSeparableproof · cited by 1
- JacobsonNoether.exists_separable_and_not_isCentralproof · cited by 1
- Polynomial.roots_expand_pow_image_iterateFrobenius_subsetproof · cited by 1
- Polynomial.roots_expand_image_iterateFrobeniusproof · cited by 0