Theorems · Theorem · commutative algebra
Submodule.fg_restrictScalars
Deprecated since 2026-01-24Use Submodule.FG.restrictScalars_of_surjective instead.
∀ {R : Type u_4} {A : Type u_5} {M : Type u_6} [inst : Semiring A] [inst_1 : AddCommMonoid M] [inst_2 : Module A M]
{S : Submodule A M} [inst_3 : CommSemiring R] [inst_4 : Algebra R A] [inst_5 : Module R M]
[inst_6 : IsScalarTower R A M], S.FG → Function.Surjective ⇑(algebraMap R A) → (Submodule.restrictScalars R S).FGAlias of Submodule.FG.restrictScalars_of_surjective.
- Defined in
- Mathlib.RingTheory.Finiteness.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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- DFunLike.coestatement · cited by 62,936
- Modulestatement · cited by 20,661
- Semiringstatement · cited by 13,802
- AddCommMonoidstatement · cited by 12,281
- Algebrastatement · cited by 11,388
- CommSemiringstatement · cited by 10,911
- RingHomstatement · cited by 10,189
- Submodulestatement · cited by 7,192
- Algebra.algebraMapstatement · cited by 4,706
- IsScalarTowerstatement · cited by 3,896
- Submodule.FGstatement · cited by 230
- Submodule.restrictScalarsstatement · cited by 180
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