Theorems · Theorem · ring theory
Module.Baer.iff_injective
∀ {R : Type u} [inst : Ring R] {Q : Type v} [inst_1 : AddCommGroup Q] [inst_2 : Module R Q] [Small.{v, u} R],
Module.Baer R Q ↔ Module.Injective R Q- Defined in
- Mathlib.Algebra.Module.Injective
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModuleSmall
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Smallstatement and proof · cited by 369
- Module.Baerstatement · cited by 20
- Module.Injectivestatement · cited by 20
- Module.Baer.of_injectiveproof · cited by 5
- Module.Baer.injectiveproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- ModuleCat.hasInjectiveDimensionLE_iff_forall_maximalSpectrumproof · cited by 2
- Module.injective_of_localization_maximalproof · cited by 2
- Module.ulift_injective_of_injectiveproof · cited by 1
- Module.Flat.iff_characterModule_baerproof · cited by 0