Theorems · Theorem · commutative algebra
IsRegular.pow_iff
∀ {R : Type u_1} [inst : Monoid R] {a : R} {n : ℕ}, 0 < n → (IsRegular (a ^ n) ↔ IsRegular a)An element a is regular if and only if a positive power of a is regular.
- Defined in
- Mathlib.Algebra.Regular.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- Monoid
Around this declaration
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Cites8
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
- IsRegularstatement and proof · cited by 116
- IsRegular.leftproof · cited by 39
- IsRegular.rightproof · cited by 19
- IsLeftRegular.powproof · cited by 5
- IsRightRegular.powproof · cited by 3
- IsLeftRegular.pow_iffproof · cited by 1
- IsRightRegular.pow_iffproof · cited by 1
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