Theorems · Theorem · ring theory
isSimpleModule_iff_isSimpleModule_of_algebraMap_surjective
∀ {S : Type u_3} [inst : Ring S] {M : Type u_4} [inst_1 : AddCommGroup M] {R : Type u_6} [inst_2 : CommRing R]
[inst_3 : Algebra R S] [inst_4 : Module R M] [inst_5 : Module S M] [IsScalarTower R S M],
Function.Surjective ⇑(algebraMap R S) → (IsSimpleModule R M ↔ IsSimpleModule S M)- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 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.
- 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
- Submoduleproof · cited by 7,192
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- IsSimpleModulestatement and proof · cited by 114
- IsSimpleOrderproof · cited by 54
Cited by1
Results whose statement or proof uses this declaration.
- Ring.ord_of_irreducibleproof · cited by 1