Theorems · Definition · order theory
Submodule.topEquiv
{R : Type u_1} → {M : Type u_3} → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → ↥⊤ ≃ₗ[R] MThe top submodule is linearly equivalent to the module.
This is the module version of AddSubmonoid.topEquiv.
- Defined in
- Mathlib.Algebra.Module.Submodule.Lattice
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topstatement and proof · cited by 9,680
- Submodulestatement · cited by 7,192
- LinearEquivstatement · cited by 3,317
- Submodule.mem_topproof · cited by 58
Cited by18
Results whose statement or proof uses this declaration.
- Submodule.annihilator_topproof · cited by 7
- ZLattice.rankproof · cited by 5
- IsSemisimpleModule.exists_linearEquiv_dfinsuppproof · cited by 3
- AffineSubspace.topEquivproof · cited by 3
- isFiniteLength_of_exists_compositionSeriesproof · cited by 3
- IsSemisimpleModule.finite_tfaeproof · cited by 2
- IsSemisimpleModule.of_injectiveproof · cited by 2
- isNoetherian_top_iffproof · cited by 2
- Module.Flat.top_mul_submoduleAlgebraproof · cited by 1
- isotypicComponent_eq_top_iffproof · cited by 1
- IsSimpleRing.tfaeproof · cited by 1
- Module.rank_le_one_iff_top_isPrincipalproof · cited by 1