Theorems · Theorem · commutative algebra
IsLeftRegular.pow_iff
∀ {R : Type u_1} [inst : Monoid R] {a : R} {n : ℕ}, 0 < n → (IsLeftRegular (a ^ n) ↔ IsLeftRegular a)An element a is left-regular if and only if a positive power of a is left-regular.
- Defined in
- Mathlib.Algebra.Regular.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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_succproof · cited by 374
- IsLeftRegularstatement and proof · cited by 97
- IsLeftRegular.powproof · cited by 5
- IsLeftRegular.of_mulproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- IsRegular.pow_iffproof · cited by 0