Theorems · Theorem · commutative algebra
Submodule.orderIsoOfAlgebraMapSurjective_symm_apply
∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : AddCommGroup M]
[inst_3 : Algebra R S] [inst_4 : Module R M] [inst_5 : Module S M] [inst_6 : IsScalarTower R S M]
(h : Function.Surjective ⇑(algebraMap R S)) (N : Submodule R M),
(RelIso.symm (Submodule.orderIsoOfAlgebraMapSurjective h)) N = { toAddSubmonoid := N.toAddSubmonoid, smul_mem' := ⋯ }- Defined in
- Mathlib.Algebra.Algebra.Tower
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- RelIsostatement · cited by 456
- RelIso.symmstatement and proof · cited by 193
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