Theorems · Theorem · commutative algebra
add_pow_expChar_pow_of_commute
∀ {R : Type u_1} [inst : Semiring R] {x y : R} (p n : ℕ) [hR : ExpChar R p],
Commute x y → (x + y) ^ p ^ n = x ^ p ^ n + y ^ p ^ n- Defined in
- Mathlib.Algebra.CharP.Lemmas
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- add_zeroproof · cited by 2,707
- Nat.Primeproof · cited by 2,059
- MulZeroClass.zero_mulproof · cited by 1,625
- CharZeroproof · cited by 932
- pow_oneproof · cited by 894
- Commutestatement and proof · cited by 639
- one_powproof · cited by 521
- CharPproof · cited by 478
- CharP.cast_eq_zeroproof · cited by 357
- ExpCharstatement and proof · cited by 276
- ExpChar.casesOnproof · cited by 21
Cited by5
Results whose statement or proof uses this declaration.
- sub_pow_expChar_pow_of_commuteproof · cited by 4
- neg_one_pow_expChar_powproof · cited by 2
- add_pow_expChar_powproof · cited by 1
- JacobsonNoether.exists_separable_and_not_isCentralproof · cited by 1
- add_pow_char_pow_of_commuteproof · cited by 0