Theorems · Theorem · commutative algebra
IsLocalRing.map_tensorProduct_mk_eq_top
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[inst_3 : IsLocalRing R] {N : Submodule R M} [Module.Finite R M],
Submodule.map ((TensorProduct.mk R (IsLocalRing.ResidueField R) M) 1) N = ⊤ ↔ N = ⊤- Defined in
- Mathlib.RingTheory.LocalRing.Module
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- Semiringproof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- AddCommMonoidproof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- RingHomproof · cited by 10,189
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- IsScalarTowerproof · cited by 3,896
Cited by4
Results whose statement or proof uses this declaration.
- IsLocalRing.subsingleton_tensorProductproof · cited by 4
- IsLocalRing.span_eq_top_of_tmul_eq_basisproof · cited by 3
- Module.exists_basis_of_span_of_maximalIdeal_rTensor_injectiveproof · cited by 2
- TensorProduct.spanFinrank_top_eq_of_residueFieldproof · cited by 1