Theorems · Theorem · commutative algebra
Ideal.mul_le_right
∀ {R : Type u} [inst : Semiring R] {I J : Ideal R}, I * J ≤ J- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 71 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.
Cites4
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.mul_mem_leftproof · cited by 107
- Ideal.mul_leproof · cited by 11
Cited by20
Results whose statement or proof uses this declaration.
- Ideal.pow_le_pow_rightproof · cited by 39
- Ideal.isCoprime_iff_codisjointproof · cited by 6
- Algebra.Generators.Cotangent.exactproof · cited by 6
- Ideal.exists_radical_pow_le_of_fgproof · cited by 4
- Ideal.sup_mul_eq_of_coprime_leftproof · cited by 4
- Ideal.quotientMulEquivQuotientProd_sndstatement · cited by 2
- not_dvd_differentIdeal_of_isCoprime_of_isSeparableproof · cited by 2
- not_dvd_differentIdeal_of_intTrace_not_memproof · 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
- Module.finite_of_surjective_of_ker_le_nilradicalproof · cited by 0
- factorPowSucc.isUnit_of_isUnit_imageproof · cited by 0