Theorems · Theorem · commutative algebra
Ideal.pow_le_pow_right
∀ {R : Type u} [inst : Semiring R] {I : Ideal R} {m n : ℕ}, m ≤ n → I ^ n ≤ I ^ m- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 75 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.
Cites9
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
- add_commproof · cited by 1,535
- le_topproof · cited by 411
- Ideal.one_eq_topproof · cited by 83
- Ideal.mul_le_rightproof · cited by 20
- Submodule.pow_zeroproof · cited by 9
- Submodule.pow_addproof · cited by 3
Cited by41
Results whose statement or proof uses this declaration.
- Ideal.pow_le_selfproof · cited by 16
- Ideal.ramificationIdx'_specproof · cited by 6
- Ideal.pow_eq_zero_of_memproof · cited by 5
- Submodule.pow_smul_top_leproof · cited by 5
- AdicCompletion.liftAlgHomstatement · cited by 5
- Ideal.ramificationIdx'_ne_one_iffproof · cited by 4
- Ideal.exists_radical_pow_le_of_fgproof · cited by 4
- Perfection.teichmullerFun_spec'proof · cited by 3
- Ideal.IsNilpotent.induction_onproof · cited by 3
- IsAdicComplete.StrictMono.factorPow_comp_eq_of_factorPow_comp_succ_eqproof · cited by 2
- Ideal.pow_succ_lt_powproof · cited by 2
- AdicCompletion.evalₐ_liftAlgHomstatement and proof · cited by 2