conjRingEquiv — Mathlib

English

The additive equivalence between spaces of linear maps is given by composing with e1 and e2.

Русский

Аддитивное эквив между пространствами линейных отображений задаётся композициями с e1 и e2.

LaTeX

$$$\text{arrowCongrAddEquiv}(e_1,e_2)\;:\;(M_1 \to_{\sigma_{11}'} M_1') \to+ (M_2 \to_{\sigma_{22}'} M_2')$$$

Lean4

/-- If `M` and `M₂` are linearly isomorphic then the endomorphism rings of `M` and `M₂`
are isomorphic.

See `LinearEquiv.conj` for the linear version of this isomorphism. -/
@[simps!]
def conjRingEquiv (e : M₁ ≃ₛₗ[σ₁₂] M₂) : Module.End R₁ M₁ ≃+* Module.End R₂ M₂
    where
  __ := arrowCongrAddEquiv e e
  map_mul' _ _ := by ext; simp [arrowCongrAddEquiv]

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