inst_ringOfIntegersAlgebra — Mathlib

English

If there is an algebra structure between two fields K and L, then the rings of integers 𝓞K and 𝓞L inherit an algebra structure making 𝓞K into an Algebra over 𝓞L.

Русский

Если между полями K и L задана алгебраическая структура, то кольца целых 𝓞K и 𝓞L наследуют алгебраическую структуру, делая 𝓞K алгебра over 𝓞L.

LaTeX

$$$\\text{inst }\\_{{\\text{ringOfIntegersAlgebra}}}: \\mathcal{O}_K \text{ is an } \\mathcal{O}_L\text{-algebra}$$$

Lean4

/-- Given an algebra structure between two fields, this instance creates an algebra structure
between their two rings of integers. -/
instance inst_ringOfIntegersAlgebra [Algebra K L] : Algebra (𝓞 K) (𝓞 L) :=
  (RingOfIntegers.mapRingHom (algebraMap K L)).toAlgebra

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