Theorems · Theorem · linear algebra
Submodule.map_dualAnnihilator_linearEquiv_flip_symm
∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[inst_3 : AddCommGroup N] [inst_4 : Module R N] [inst_5 : Module.IsReflexive R M] (e : N ≃ₗ[R] Module.Dual R M)
(p : Submodule R N), Submodule.map (↑e.flip.symm) p.dualAnnihilator = (Submodule.map (↑e) p).dualCoannihilator- Cited by
- 0 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
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- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapproof · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- LinearEquivstatement and proof · cited by 3,317
- LinearEquiv.symmstatement · cited by 1,461
- LinearEquiv.toLinearMapstatement and proof · cited by 1,171
- Submodule.mapstatement and proof · cited by 614
- Module.Dualstatement and proof · cited by 583
- Submodule.dualAnnihilatorstatement · cited by 77
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