Theorems · Theorem · ring theory

TrivSqZeroExt.liftEquiv_apply

∀ {S : Type u_1} {R : Type u} {M : Type v} [inst : CommSemiring S] [inst_1 : Semiring R] [inst_2 : AddCommMonoid M]
  [inst_3 : Algebra S R] [inst_4 : Module S M] [inst_5 : Module R M] [inst_6 : Module Rᵐᵒᵖ M]
  [inst_7 : SMulCommClass R Rᵐᵒᵖ M] [inst_8 : IsScalarTower S R M] [inst_9 : IsScalarTower S Rᵐᵒᵖ M] {A : Type u_2}
  [inst_10 : Semiring A] [inst_11 : Algebra S A]
  (fg :
    { fg //
      (∀ (x y : M), fg.2 x * fg.2 y = 0) ∧
        (∀ (r : R) (x : M), fg.2 (r • x) = fg.1 r * fg.2 x) ∧
          ∀ (r : R) (x : M), fg.2 (MulOpposite.op r • x) = fg.2 x * fg.1 r }),
  TrivSqZeroExt.liftEquiv fg = TrivSqZeroExt.lift (↑fg).1 (↑fg).2 ⋯ ⋯ ⋯

Defined in

Mathlib.Algebra.TrivSqZeroExt.Basic

Cited by

0 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAddCommMonoidAlgebraModuleModuleModuleSMulCommClassIsScalarTowerIsScalarTowerSemiringAlgebra