CyclotomicRing — Mathlib

English

There is a canonical IsCyclotomicExtension description in terms of adjoin and primitive roots.

Русский

Существует каноническое описание IsCyclotomicExtension через адъюнкт и примитивные корни.

LaTeX

$$$IsCyclotomicExtension(S,K,L) = \\text{adjoin and roots description}$$$

Lean4

/-- If `A` is a domain with fraction field `K` and `n : ℕ`, we define `CyclotomicRing n A K` as
the `A`-subalgebra of `CyclotomicField n K` generated by the roots of `X ^ n - 1`. If `n`
is nonzero in `A`, it has the instance `IsCyclotomicExtension {n} A (CyclotomicRing n A K)`. -/
@[nolint unusedArguments]
def CyclotomicRing : Type w :=
  adjoin A {b : CyclotomicField n K | b ^ n = 1}

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