Theorems · Theorem · commutative algebra
Submodule.map_subtype_top
∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(p : Submodule R M), Submodule.map p.subtype ⊤ = pUnder the canonical linear map from a submodule p to the ambient space M, the image of the
maximal submodule of p is just p.
- Defined in
- Mathlib.Algebra.Module.Submodule.Range
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Submodule.mapstatement · cited by 614
- Submodule.subtypestatement and proof · cited by 480
- Submodule.map_topproof · cited by 105
- Submodule.range_subtypeproof · cited by 82
Cited by9
Results whose statement or proof uses this declaration.
- Submodule.comap_subtype_eq_topproof · cited by 5
- ZLattice.rankproof · cited by 5
- Ideal.map_toCotangent_kerproof · cited by 2
- Submodule.exists_eq_colon_of_mem_minimalPrimesproof · cited by 1
- Module.End.iSup_maxGenEigenspace_eq_topproof · cited by 1
- LinearMap.IsSymmetric.iSup_eigenspace_inf_eigenspace_of_commuteproof · cited by 1
- Submodule.span_range_inclusionSpanproof · cited by 1
- Submodule.span_range_inclusion_eq_topproof · cited by 1
- LieSubalgebra.normalizer_eq_self_of_engel_leproof · cited by 0