Theorems · Theorem · commutative algebra
Ideal.mul_le_inf
∀ {R : Type u} [inst : Semiring R] {I J : Ideal R} [I.IsTwoSided], I * J ≤ I ⊓ J- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Idealstatement and proof · cited by 4,748
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.mul_mem_leftproof · cited by 107
- Ideal.mul_mem_rightproof · cited by 71
- Ideal.mul_leproof · cited by 11
Cited by10
Results whose statement or proof uses this declaration.
- Ideal.le_of_dvdproof · cited by 9
- Ideal.sup_iInf_eq_topproof · cited by 5
- Ideal.IsPrime.inf_leproof · cited by 3
- Ideal.radical_mulproof · cited by 2
- Ideal.mul_eq_inf_of_coprimeproof · cited by 2
- injective_lTensor_quotient_iff_inf_eq_mulproof · cited by 2
- Ideal.multiset_prod_le_infproof · cited by 1
- Submodule.exists_eq_colon_of_mem_minimalPrimesproof · cited by 1
- Algebra.FormallySmooth.of_surjective_of_ker_eq_map_of_flatproof · cited by 1
- Ideal.inf_ne_bot_of_ne_botproof · cited by 0