Theorems · Theorem · ring theory
IsLeftRegular.pow_injective
∀ {R : Type u_1} [inst : Monoid R] {r : R} [IsMulTorsionFree R],
IsLeftRegular r → r ≠ 1 → Function.Injective fun n => r ^ n- Defined in
- Mathlib.Algebra.Ring.NonZeroDivisors
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidIsMulTorsionFree
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- pow_addproof · cited by 315
- IsLeftRegularstatement and proof · cited by 97
- IsMulTorsionFreestatement and proof · cited by 44
- IsLeftRegular.powproof · cited by 5
- IsLeftRegular.mul_left_eq_self_iffproof · cited by 1
- pow_eq_one_iff_rightproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- IsMulTorsionFree.pow_right_injective₀proof · cited by 2
- Ideal.relNorm_eq_pow_of_isPrime_isGaloisproof · cited by 1
- IsMulTorsionFree.pow_right_injectiveproof · cited by 1
- IsRightRegular.pow_injectiveproof · cited by 0