Theorems · Theorem · commutative algebra
FractionalIdeal.zero_mem
∀ {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), 0 ∈ I- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement and proof · cited by 423
- FractionalIdeal.coeToSubmoduleproof · cited by 130
- Submodule.zero_memproof · cited by 58
Cited by4
Results whose statement or proof uses this declaration.
- FractionalIdeal.le_one_iff_exists_coeIdealproof · cited by 5
- FractionalIdeal.zero_leproof · cited by 5
- FractionalIdeal.extended_oneproof · cited by 0
- FractionalIdeal.extended_addproof · cited by 0