Theorems · Theorem · commutative algebra

Module.mem_support_mono

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  {p q : PrimeSpectrum R}, p ≤ q → p ∈ Module.support R M → q ∈ Module.support R M

Defined in: Mathlib.RingTheory.Support
Cited by: 4 results in Mathlib
Foundations: Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module

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Cites8

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
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LE.le.transproof · cited by 3,151
PrimeSpectrumstatement and proof · cited by 625
Module.supportstatement and proof · cited by 52
Module.mem_support_iff_exists_annihilatorproof · cited by 4

Cited by4

Results whose statement or proof uses this declaration.

Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobsonproof · cited by 2
IsLocalRing.closedPoint_mem_supportproof · cited by 1
Module.exists_ltSeries_support_isMaximal_last_of_ltSeries_supportproof · cited by 1
Module.stableUnderSpecialization_supportproof · cited by 0