Theorems · Theorem · commutative algebra
Ideal.Quotient.mk_eq_mk
∀ {R : Type u} [inst : Ring R] {I : Ideal R} [inst_1 : I.IsTwoSided] (x : R),
Submodule.Quotient.mk x = (Ideal.Quotient.mk I) x- Defined in
- Mathlib.RingTheory.Ideal.Quotient.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 83 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.Quotient.mkstatement · cited by 610
- Submodule.Quotient.mkstatement · cited by 184
- Ideal.IsTwoSidedstatement and proof · cited by 179
Cited by7
Results whose statement or proof uses this declaration.
- Module.p_pow_smul_liftproof · cited by 1
- Ideal.Quotient.span_singleton_oneproof · cited by 1
- Module.torsion_by_prime_power_decompositionproof · cited by 1
- Ideal.Quotient.torsionBy_eq_span_singletonproof · cited by 1
- AdicCompletion.Ideal.mk_eq_mkproof · cited by 1
- Ideal.quotientToQuotientRangePowQuotSucc_injectiveproof · cited by 0
- Ideal.quotientToQuotientRangePowQuotSucc_surjectiveproof · cited by 0