Theorems · Theorem · commutative algebra
FractionalIdeal.num_zero_eq
∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P],
Function.Injective ⇑(algebraMap R P) → FractionalIdeal.num 0 = 0- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealstatement · cited by 4,748
- Bot.botproof · cited by 4,720
- Algebra.algebraMapstatement and proof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement · cited by 423
- Submodule.comapproof · cited by 347
- Algebra.linearMapproof · cited by 157
- FractionalIdeal.numstatement · cited by 22
Cited by2
Results whose statement or proof uses this declaration.
- FractionalIdeal.num_eq_zero_iffproof · cited by 3
- FractionalIdeal.num_le_mul_invproof · cited by 1