Theorems · Theorem · linear algebra
Submodule.dualAnnihilator_eq_bot_iff
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {W : Submodule R M}
[Module.Projective R (M ⧸ W)], W.dualAnnihilator = ⊥ ↔ W = ⊤- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- Bot.botstatement · cited by 4,720
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Module.Dualstatement · cited by 583
- Module.Projectivestatement and proof · cited by 82
- Submodule.dualAnnihilatorstatement · cited by 77
- Submodule.Quotient.subsingleton_iffproof · cited by 8
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