Theorems · Theorem · commutative algebra
pow_inj_of_not_isUnit
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {q : M},
¬IsUnit q → q ≠ 0 → ∀ {m n : ℕ}, q ^ m = q ^ n ↔ m = n- Defined in
- Mathlib.Algebra.Prime.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsUnitstatement and proof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- IsCancelMulZerostatement and proof · cited by 177
- pow_injective_of_not_isUnitproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.pow_succ_lt_powproof · cited by 2