Theorems · Theorem · commutative algebra
Ideal.Filtration.pow_smul_le
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {I : Ideal R}
(F : I.Filtration M) (i j : ℕ), I ^ i • F.N j ≤ F.N (i + j)- Defined in
- Mathlib.RingTheory.Filtration
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement and proof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- LE.le.transproof · cited by 3,151
- zero_addproof · cited by 2,366
- add_commproof · cited by 1,535
- pow_zeroproof · cited by 1,094
- add_assocproof · cited by 746
- SemigroupAction.mul_smulproof · cited by 291
- pow_succ'proof · cited by 228
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.Filtration.pow_smul_le_pow_smulproof · cited by 1