Theorems · Definition · commutative algebra
FractionalIdeal.num
{R : Type u_1} →
[inst : CommRing R] →
{S : Submonoid R} → {P : Type u_2} → [inst_1 : CommRing P] → [inst_2 : Algebra R P] → FractionalIdeal S P → Ideal RAn ideal of R such that I.den • I = I.num, see FractionalIdeal.den and
FractionalIdeal.den_mul_self_eq_num.
- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement · cited by 4,748
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement and proof · cited by 423
- Submodule.comapproof · cited by 347
- Algebra.linearMapproof · cited by 157
- FractionalIdeal.coeToSubmoduleproof · cited by 130
- FractionalIdeal.denproof · cited by 19
Cited by27
Results whose statement or proof uses this declaration.
- FractionalIdeal.absNormproof · cited by 19
- FractionalIdeal.den_mul_self_eq_num'statement and proof · cited by 5
- FractionalIdeal.equivNumstatement · cited by 4
- FractionalIdeal.den_mul_self_eq_numstatement and proof · cited by 4
- FractionalIdeal.num_eq_zero_iffstatement and proof · cited by 3
- FractionalIdeal.equivNumOfIsLocalizationstatement · cited by 2
- FractionalIdeal.absNorm_eqstatement · cited by 2
- FractionalIdeal.absNorm_eq'proof · cited by 2
- FractionalIdeal.zero_of_num_eq_botstatement and proof · cited by 2
- FractionalIdeal.absNorm_nonnegproof · cited by 2
- ClassGroup.integralRepproof · cited by 2
- ClassGroup.integralRep_mem_nonZeroDivisorsstatement and proof · cited by 2