Theorems · Theorem · commutative algebra

Module.Flat.iff_flat_tensorProduct

∀ (R : Type u) (M : Type v) [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (S : Type u_1)
  [inst_3 : CommRing S] [inst_4 : Algebra R S] [Module.FaithfullyFlat R S],
  Module.Flat S (TensorProduct R S M) ↔ Module.Flat R M

Defined in: Mathlib.RingTheory.Flat.FaithfullyFlat.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module CommRing Algebra Module.FaithfullyFlat

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Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Algebrastatement and proof · cited by 11,388
TensorProductstatement and proof · cited by 2,545
Module.Flatstatement and proof · cited by 279
Module.FaithfullyFlatstatement and proof · cited by 72
Module.Flat.of_flat_tensorProductproof · cited by 2

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