Theorems · Theorem · commutative algebra

Module.Invertible.tensorProductComm_eq_refl

∀ (R : Type u) (M : Type v) [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [Module.Invertible R M], TensorProduct.comm R M M = LinearEquiv.refl R (TensorProduct R M M)

Defined in: Mathlib.RingTheory.PicardGroup
Cited by: 1 results in Mathlib
Foundations: Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid Module Module.Invertible

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Cites44

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
LinearMapproof · cited by 10,215
Idealproof · cited by 4,748
mul_oneproof · cited by 3,885
LinearEquivstatement and proof · cited by 3,317
TensorProductstatement and proof · cited by 2,545
mul_commproof · cited by 2,262
LinearMap.compproof · cited by 1,642

Cited by1

Results whose statement or proof uses this declaration.

Module.Invertible.tmul_commproof · cited by 0