Theorems · Theorem · commutative algebra
Ideal.pow_right_mono
∀ {R : Type u} [inst : Semiring R] {I J : Ideal R}, I ≤ J → ∀ (n : ℕ), I ^ n ≤ J ^ n- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- le_reflproof · cited by 2,061
- Submodule.pow_zeroproof · cited by 9
- Submodule.pow_succproof · cited by 6
- Ideal.mul_monoproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Algebra.FormallySmooth.comp_surjectiveproof · cited by 6
- IsUnramifiedAt.of_liesOver_of_ne_botproof · cited by 1
- IsHausdorff.of_mapproof · cited by 0
- WithIdeal.uniformContinuous_of_map_leproof · cited by 0
- Ideal.exists_pow_le_of_le_radical_of_fg_radicalproof · cited by 0