Theorems · Theorem · commutative algebra
FractionalIdeal.isFractional_of_le
∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
{I : Submodule R P} {J : FractionalIdeal S P}, I ≤ ↑J → IsFractional S I- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 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
- Submodulestatement and proof · cited by 7,192
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement and proof · cited by 423
- FractionalIdeal.coeToSubmodulestatement and proof · cited by 130
- IsLocalization.IsIntegerproof · cited by 39
- IsFractionalstatement · cited by 29
- FractionalIdeal.isFractionalproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.isNoetherian_iffproof · cited by 2