Theorems · Theorem · commutative algebra
FractionalIdeal.den_mul_self_eq_num
∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
(I : FractionalIdeal S P), I.den • ↑I = Submodule.map (Algebra.linearMap R P) I.num- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Idealproof · cited by 4,748
- Submonoidstatement and proof · cited by 3,086
- Submodule.mapstatement and proof · cited by 614
- FractionalIdealstatement and proof · cited by 423
- Algebra.linearMapstatement and proof · cited by 157
- FractionalIdeal.coeToSubmodulestatement and proof · cited by 130
Cited by4
Results whose statement or proof uses this declaration.
- FractionalIdeal.den_mul_self_eq_num'proof · cited by 5
- FractionalIdeal.zero_of_num_eq_botproof · cited by 2
- FractionalIdeal.den_mem_invproof · cited by 1
- FractionalIdeal.absNorm_div_norm_eq_absNorm_div_normproof · cited by 1