Theorems · Definition · commutative algebra

HahnSeries.embDomainAlgHom

{Γ : Type u_1} →
  {R : Type u_3} →
    [inst : AddCommMonoid Γ] →
      [inst_1 : PartialOrder Γ] →
        [inst_2 : IsOrderedCancelAddMonoid Γ] →
          [inst_3 : CommSemiring R] →
            {A : Type u_6} →
              [inst_4 : Semiring A] →
                [inst_5 : Algebra R A] →
                  {Γ' : Type u_7} →
                    [inst_6 : AddCommMonoid Γ'] →
                      [inst_7 : PartialOrder Γ'] →
                        [inst_8 : IsOrderedCancelAddMonoid Γ'] →
                          (f : Γ →+ Γ') →
                            Function.Injective ⇑f →
                              (∀ (g g' : Γ), f g ≤ f g' ↔ g ≤ g') → HahnSeries Γ A →ₐ[R] HahnSeries Γ' A

Extending the domain of Hahn series is an algebra homomorphism.

Defined in

Mathlib.RingTheory.HahnSeries.Multiplication

Cited by

1 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidPartialOrderIsOrderedCancelAddMonoidCommSemiringSemiringAlgebraAddCommMonoidPartialOrderIsOrderedCancelAddMonoid