Theorems · Definition · commutative algebra

Module.Flat.submoduleAlgebra

{R : Type u} →
  {M : Type v} →
    {A : Type u_4} →
      [inst : CommSemiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] →
            [inst_3 : Semiring A] → [inst_4 : Algebra R A] → (TensorProduct R A M ≃ₗ[A] A) → Submodule R A

A flat R-module as a R-submodule of a faithful R-algebra.

Defined in

Mathlib.RingTheory.PicardGroup

Cited by

5 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleSemiringAlgebra