Theorems · Theorem · commutative algebra
FractionalIdeal.coeIdeal_mul
∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
(I J : Ideal R), ↑(I * J) = ↑I * ↑J- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement and proof · cited by 4,748
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement · cited by 423
- FractionalIdeal.coeToSubmoduleproof · cited by 130
- FractionalIdeal.coeIdealstatement and proof · cited by 109
- FractionalIdeal.coeToSubmodule_injectiveproof · cited by 19
- FractionalIdeal.isFractionalproof · cited by 6
- FractionalIdeal.mul_defproof · cited by 6
- IsFractional.mulproof · cited by 3
- IsLocalization.coeSubmodule_mulproof · cited by 1
Cited by14
Results whose statement or proof uses this declaration.
- Ideal.dvd_iff_leproof · cited by 33
- FractionalIdeal.count_well_definedproof · cited by 5
- FractionalIdeal.count_mulproof · cited by 4
- FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdealproof · cited by 3
- FractionalIdeal.coeIdealHomproof · cited by 3
- differentIdeal_eq_differentIdeal_mul_differentIdealproof · cited by 3
- not_dvd_differentIdeal_of_intTrace_not_memproof · cited by 1
- dvd_differentIdeal_of_not_isSeparableproof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_neg_mulproof · cited by 1
- pow_sub_one_dvd_differentIdeal_auxproof · cited by 1
- conductor_mul_differentIdealproof · cited by 1
- IsDedekindDomain.exists_add_spanSingleton_mul_eqproof · cited by 1