Theorems · Theorem · commutative algebra
IsRegular.pow
∀ {R : Type u_1} [inst : Monoid R] {a : R} (n : ℕ), IsRegular a → IsRegular (a ^ n)Any power of a regular element is regular.
- Defined in
- Mathlib.Algebra.Regular.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.IsHadamard.of_mul_conjTransposeproof · cited by 1
- MvPolynomial.isRegular_X_powproof · cited by 0
- Matrix.IsHadamard.isRegular_detproof · cited by 0