Theorems · Theorem · commutative algebra
Ideal.mul_le_left
∀ {R : Type u} [inst : Semiring R] {I J : Ideal R} [I.IsTwoSided], I * J ≤ I- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 19 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.
Cites5
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_rightproof · cited by 71
- Ideal.mul_leproof · cited by 11
Cited by19
Results whose statement or proof uses this declaration.
- Ideal.exists_radical_pow_le_of_fgproof · cited by 4
- Ideal.IsTwoSided.mul_oneproof · cited by 3
- Ideal.mul_iInfproof · cited by 3
- Ideal.sup_mul_eq_of_coprime_rightproof · cited by 3
- IsDedekindDomain.exists_sup_span_eqproof · cited by 2
- Ideal.isOka_isPrincipalproof · cited by 1
- Polynomial.contentIdeal_le_contentIdeal_of_dvdproof · cited by 1
- AdicCompletion.surjective_evalₐproof · cited by 1
- Ideal.sup_pow_add_le_pow_sup_powproof · cited by 1
- PrimeSpectrum.exists_primeSpectrum_prod_le_and_ne_bot_of_domainproof · cited by 1
- Ideal.fst_comp_quotientMulEquivQuotientProdstatement · cited by 0
- Polynomial.contentIdeal_eq_top_of_contentIdeal_mul_eq_topproof · cited by 0