Theorems · Theorem · commutative algebra
Ideal.decomposition_erase_inf
Deprecated since 2026-01-19Use Submodule.decomposition_erase_inf instead.
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{N : Submodule R M} {s : Finset (Submodule R M)},
s.inf id = N → ∃ t ⊆ s, t.inf id = N ∧ ∀ ⦃J : Submodule R M⦄, J ∈ t → ¬(t.erase J).inf id ≤ JAlias of Submodule.decomposition_erase_inf.
- Defined in
- Mathlib.RingTheory.Lasker
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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- Modulestatement · cited by 20,661
- Finsetstatement · cited by 13,712
- AddCommMonoidstatement · cited by 12,281
- CommSemiringstatement · cited by 10,911
- Submodulestatement · cited by 7,192
- Finset.erasestatement · cited by 455
- Finset.infstatement · cited by 219
- Submodule.decomposition_erase_infproof · cited by 2
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