Theorems · Theorem · commutative algebra

IsLocalRing.map_mkQ_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 (IsLocalRing.maximalIdeal R • ⊤).mkQ N = ⊤ ↔ N = ⊤

Defined in: Mathlib.RingTheory.LocalRing.Module
Cited by: 1 results in Mathlib
Foundations: Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module IsLocalRing Module.Finite

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites18

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
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Top.topstatement and proof · cited by 9,680
Submodulestatement and proof · cited by 7,192
Idealstatement · cited by 4,748
HasQuotient.Quotientstatement and proof · cited by 2,301
Module.Finitestatement and proof · cited by 1,032
Submodule.mapstatement and proof · cited by 614
le_topproof · cited by 411
IsLocalRingstatement and proof · cited by 339

Cited by1

Results whose statement or proof uses this declaration.

IsLocalRing.map_tensorProduct_mk_eq_topproof · cited by 4