Theorems · Theorem · commutative algebra
Module.Finite.of_restrictScalars_finite
∀ (R : Type u_6) (A : Type u_7) (M : Type u_8) [inst : Semiring R] [inst_1 : Semiring A] [inst_2 : AddCommMonoid M] [inst_3 : Module R M] [inst_4 : Module A M] [inst_5 : SMul R A] [IsScalarTower R A M] [hM : Module.Finite R M], Module.Finite A M
- Defined in
- Mathlib.RingTheory.Finiteness.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topproof · cited by 9,680
- Submoduleproof · cited by 7,192
- IsScalarTowerstatement and proof · cited by 3,896
- Set.Finiteproof · cited by 1,814
- Submodule.spanproof · cited by 1,504
- Module.Finitestatement and proof · cited by 1,032
- eq_top_iffproof · cited by 236
- Submodule.restrictScalarsproof · cited by 180
Cited by12
Results whose statement or proof uses this declaration.
- not_dvd_differentIdeal_of_isCoprime_of_isSeparableproof · cited by 2
- RingHom.Finite.of_comp_finiteproof · cited by 2
- Algebra.QuasiFiniteAt.exists_basicOpen_eq_singletonproof · cited by 2
- FunctionField.FiniteDimensional.adjoin_algebraMap_Xproof · cited by 1
- dvd_differentIdeal_of_not_isSeparableproof · cited by 1
- IsGaloisGroup.finiteproof · cited by 1
- IsLocalRing.finrank_quotient_mapproof · cited by 1
- Module.Finite.of_equiv_equivproof · cited by 1
- Algebra.FormallySmooth.iff_injective_lTensor_residueFieldproof · cited by 1
- NumberField.InfinitePlace.card_monoproof · cited by 0
- Ring.HasFiniteQuotients.of_module_finiteproof · cited by 0
- Module.free_quotSMulTop_iff_freeproof · cited by 0