Theorems · Theorem · ring theory
Module.Baer.of_injective
∀ {R : Type u} [inst : Ring R] {Q : Type v} [inst_1 : AddCommGroup Q] [inst_2 : Module R Q] [Small.{v, u} R],
Module.Injective R Q → Module.Baer R Q- Defined in
- Mathlib.Algebra.Module.Injective
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 28 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.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idproof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapproof · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Idealproof · cited by 4,748
- LinearEquivproof · cited by 3,317
- LinearMap.compproof · cited by 1,642
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.toLinearMapproof · cited by 1,171
- Submodule.subtypeproof · cited by 480
Cited by5
Results whose statement or proof uses this declaration.
- Module.Baer.iff_injectiveproof · cited by 4
- Module.injective_of_isLocalizedModuleproof · cited by 2
- Module.injective_of_localization_maximalproof · cited by 2
- Module.Injective.of_ringEquivproof · cited by 1
- Module.Injective.extension_propertyproof · cited by 0