Theorems · Theorem · commutative algebra

IsLocalRing.map_mkQ_eq

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : IsLocalRing R] {N₁ N₂ : Submodule R M},
  N₁ ≤ N₂ →
    N₂.FG →
      (Submodule.map (IsLocalRing.maximalIdeal R • N₂).mkQ N₁ = Submodule.map (IsLocalRing.maximalIdeal R • N₂).mkQ N₂ ↔
        N₁ = N₂)

Defined in: Mathlib.RingTheory.LocalRing.Module
Cited by: 1 results in Mathlib
Foundations: Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module IsLocalRing

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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
Submodulestatement and proof · cited by 7,192
Idealstatement and proof · cited by 4,748
Bot.botproof · cited by 4,720
HasQuotient.Quotientstatement · cited by 2,301
le_reflproof · cited by 2,061
Submodule.mapstatement and proof · cited by 614
LE.le.antisymmproof · cited by 507
Eq.geproof · cited by 375

Cited by1

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IsLocalRing.map_mkQ_eq_topproof · cited by 1