Theorems · Theorem · commutative algebra
Ideal.mk_ker
∀ {R : Type u} [inst : Ring R] {I : Ideal R} [inst_1 : I.IsTwoSided], RingHom.ker (Ideal.Quotient.mk I) = I- Cited by
- 59 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.Quotient.mkstatement and proof · cited by 610
- RingHom.kerstatement · cited by 363
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Ideal.extproof · cited by 131
- Ideal.Quotient.eq_zero_iff_memproof · cited by 74
- Submodule.mem_botproof · cited by 55
- Ideal.mem_comapproof · cited by 54
Cited by59
Results whose statement or proof uses this declaration.
- Ideal.Quotient.mkₐ_kerproof · cited by 5
- Ideal.isPrime_map_quotientMk_of_isPrimeproof · cited by 4
- Ideal.isRadical_iff_quotient_reducedproof · cited by 4
- Ideal.bot_quotient_isMaximal_iffproof · cited by 3
- AdicCompletion.isMaximal_map_of_leproof · cited by 3
- Ideal.mem_quotient_iff_mem_supproof · cited by 3
- IsLocalRing.exists_maximalIdeal_pow_le_of_isArtinianRing_quotientproof · cited by 2
- Ideal.minimalPrimes_eq_comapproof · cited by 2
- MvPolynomial.eval₂_C_mk_eq_zeroproof · cited by 2
- Ideal.exists_ideal_over_prime_of_isIntegral_of_isPrimeproof · cited by 2
- Ideal.jacobson_eq_iff_jacobson_quotient_eq_botproof · cited by 2
- Algebra.weaklyQuasiFiniteAt_iffproof · cited by 2