Theorems · Theorem · commutative algebra

TensorProduct.exists_of_fg

∀ {R : Type u} {M : Type u_1} {N : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : AddCommMonoid N] [inst_4 : Module R N] (u : TensorProduct R M N),
  ∃ P, P.FG ∧ u ∈ (LinearMap.rTensor N P.subtype).range

Defined in: Mathlib.RingTheory.TensorProduct.DirectLimitFG
Cited by: 2 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid Module AddCommMonoid Module

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Cites19

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 · cited by 18,349
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
Submodulestatement and proof · cited by 7,192
TensorProductstatement and proof · cited by 2,545
LinearEquiv.symmproof · cited by 1,461
LinearMap.rangestatement and proof · cited by 893
Submodule.subtypestatement and proof · cited by 480
LinearMap.rTensorstatement and proof · cited by 266
Submodule.FGstatement and proof · cited by 230

Cited by2

Results whose statement or proof uses this declaration.

TensorProduct.Algebra.exists_of_fgproof · cited by 3
TensorProduct.Algebra.eq_of_fg_of_subtype_eqproof · cited by 2