Theorems · Theorem · commutative algebra
Module.mem_support_iff_nontrivial_residueField_tensorProduct
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Finite R M]
(p : PrimeSpectrum R), p ∈ Module.support R M ↔ Nontrivial (TensorProduct R p.asIdeal.ResidueField M)- Defined in
- Mathlib.RingTheory.LocalRing.Module
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearEquivproof · cited by 3,317
- TensorProductstatement and proof · cited by 2,545
- Nontrivialstatement and proof · cited by 2,416
- LinearEquiv.symmproof · cited by 1,461
- Module.Finitestatement and proof · cited by 1,032
- PrimeSpectrumstatement and proof · cited by 625
- Ideal.primeComplstatement and proof · cited by 462
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