Theorems · Theorem · commutative algebra

Module.FinitePresentation.trans

∀ (R : Type u_2) (M : Type u_3) [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] [inst_5 : Module S M] [IsScalarTower R S M]
  [Module.FinitePresentation R S] [Module.FinitePresentation S M], Module.FinitePresentation R M

Defined in: Mathlib.Algebra.Module.FinitePresentation
Cited by: 1 results in Mathlib
Foundations: Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module CommRing Algebra Module IsScalarTower Module.FinitePresentation Module.FinitePresentation

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Cites29

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.idproof · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Algebrastatement and proof · cited by 11,388
LinearMapproof · cited by 10,215
Submoduleproof · cited by 7,192
IsScalarTowerstatement and proof · cited by 3,896
LinearEquivproof · cited by 3,317
HasQuotient.Quotientproof · cited by 2,301
LinearMap.compproof · cited by 1,642

Cited by1

Results whose statement or proof uses this declaration.

Module.FinitePresentation.of_finite_of_finitePresentationproof · cited by 2