Theorems · Theorem · commutative algebra
FractionalIdeal.mul_def
∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
(I J : FractionalIdeal S P), I * J = ⟨↑I * ↑J, ⋯⟩- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 · cited by 7,192
- Submonoidstatement and proof · cited by 3,086
- FractionalIdealstatement and proof · cited by 423
- FractionalIdeal.coeToSubmodulestatement and proof · cited by 130
- IsFractionalstatement · cited by 29
- FractionalIdeal.isFractionalstatement and proof · cited by 6
- IsFractional.mulstatement and proof · cited by 3
- FractionalIdeal.mul_def'proof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- FractionalIdeal.coe_mulproof · cited by 15
- FractionalIdeal.coeIdeal_mulproof · cited by 13
- FractionalIdeal.mul_mem_mulproof · cited by 6
- FractionalIdeal.mul_induction_onproof · cited by 2
- FractionalIdeal.mul_leproof · cited by 1
- FractionalIdeal.map_mulproof · cited by 0