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Theorems · Theorem · commutative algebra

isNoetherian_of_le

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {s t : Submodule R M} [ht : IsNoetherian R ↥t], s ≤ t → IsNoetherian R ↥s
Defined in
Mathlib.RingTheory.Noetherian.Defs
Cited by
2 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringAddCommMonoidModuleIsNoetherian
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Around this declaration

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

LinearMap.HasNoetherianRange.add · cited by 2HasNoetherianRange.addLinearMap.HasNoetherianRange.comp_right · cited by 2HasNoetherianRange.comp_r…Module · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidSubmodule · cited by 7192Submodulele_trans · cited by 985le_transIsNoetherian · cited by 208IsNoetherianisNoetherian_submodule · cited by 8isNoetherian_submoduleisNoetherian_of_leCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.