Theorems · Definition · linear algebra

RingHom.polyToMatrix

{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : Semiring A] →
        {n : Type w} →
          [inst_2 : DecidableEq n] →
            [inst_3 : Fintype n] → (A →+* Matrix n n R) → Polynomial A →+* Matrix n n (Polynomial R)

Extend a ring hom A → Mₙ(R) to a ring hom A[X] → Mₙ(R[X]).

Defined in

Mathlib.RingTheory.MatrixPolynomialAlgebra

Cited by

5 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringDecidableEqFintype