Theorems · Theorem · commutative algebra
LinearMap.range_id
∀ {R : Type u_1} {M : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
LinearMap.id.range = ⊤- Defined in
- Mathlib.Algebra.Module.Submodule.Range
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 26 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 and proof · cited by 9,680
- Submodulestatement · cited by 7,192
- LinearMap.rangestatement and proof · cited by 893
- LinearMap.idstatement and proof · cited by 625
- SetLike.coe_injectiveproof · cited by 374
- Set.range_idproof · cited by 37
Cited by9
Results whose statement or proof uses this declaration.
- Submodule.image_smul_top_eq_range_lsumproof · cited by 2
- MeasureTheory.ae_ae_add_linearMap_mem_iffproof · cited by 1
- AdicCompletion.map_surjective_of_mkQ_comp_surjectiveproof · cited by 1
- Matrix.rank_oneproof · cited by 1
- Submodule.isTopCompl_top_botproof · cited by 1
- LinearMap.normDet_comp_of_finrank_eqproof · cited by 1
- LinearMap.FiniteRangeSetoid.equiv_of_eqOn_of_isNoetherianproof · cited by 0
- LinearMap.IsProj.submodule_eq_top_iffproof · cited by 0
- LinearMap.index_idproof · cited by 0