Theorems · Inductive type · group theory

RootableBy

(A : Type u_1) → (α : Type u_2) → [Monoid A] → [Pow A α] → [Zero α] → Type (max u_1 u_2)

A Monoid A is α-rootable iff xⁿ = a has a solution for all n ≠ 0 ∈ α and a ∈ A. Here we adopt a constructive approach where we ask an explicit root : A → α → A function such that * root a 0 = 1 for all a ∈ A * (root a n)ⁿ = a for all n ≠ 0 ∈ α and a ∈ A.

Defined in

Mathlib.GroupTheory.Divisible

Cited by

6 results in Mathlib

Foundations

Depth 1 from the axioms · uses no axioms

Assumes

MonoidPowZero