Theorems · Theorem · commutative algebra
Submodule.spanRank_restrictScalars_eq
∀ {R : Type u_1} {S : Type u_2} {M : Type u} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : AddCommMonoid M]
[inst_3 : Algebra R S] [inst_4 : Module R M] [inst_5 : Module S M] [inst_6 : IsScalarTower R S M],
Function.Surjective ⇑(algebraMap R S) → ∀ (N : Submodule S M), (Submodule.restrictScalars R N).spanRank = N.spanRank- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites24
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- DFunLike.coestatement and proof · cited by 62,936
- 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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Submodulestatement and proof · cited by 7,192
- Set.Elemproof · cited by 7,166
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
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