Theorems · Theorem · commutative algebra
Submodule.annihilator_sup
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(N P : Submodule R M), (N ⊔ P).annihilator = N.annihilator ⊓ P.annihilator- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
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Cites13
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- iInfproof · cited by 1,690
- iSup_subtype'proof · cited by 44
- sSup_eq_iSupproof · cited by 42
- Submodule.annihilatorstatement and proof · cited by 42
- iInf_subtype'proof · cited by 34
- sSup_pairproof · cited by 11
- iInf_pairproof · cited by 2
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