Theorems · Theorem · commutative algebra
IsSMulRegular.linearMap_subsingleton_of_mem_annihilator
∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup N]
[inst_3 : Module R M] [inst_4 : Module R N] {r : R},
IsSMulRegular M r → r ∈ Module.annihilator R N → Subsingleton (N →ₗ[R] M)- Defined in
- Mathlib.RingTheory.Regular.LinearMap
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Idealstatement · cited by 4,748
- map_zeroproof · cited by 1,614
- LinearMap.extproof · cited by 844
- smul_zeroproof · cited by 665
- map_smulproof · cited by 566
- IsSMulRegularstatement and proof · cited by 128
Cited by1
Results whose statement or proof uses this declaration.
- IsSMulRegular.subsingleton_linearMap_iffproof · cited by 2