Theorems · Theorem · commutative algebra
IsFractional.mul
∀ {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 : Submodule R P}, IsFractional S I → IsFractional S J → IsFractional S (I * J)- Defined in
- Mathlib.RingTheory.FractionalIdeal.Basic
- Cited by
- 3 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.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Submodulestatement and proof · cited by 7,192
- Algebra.algebraMapproof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- mul_commproof · cited by 2,262
- SemigroupAction.mul_smulproof · cited by 291
- Algebra.smul_defproof · cited by 287
- smul_addproof · cited by 263
- Submodule.smul_memproof · cited by 204
- smul_mul_assocproof · cited by 77
Cited by3
Results whose statement or proof uses this declaration.
- FractionalIdeal.coeIdeal_mulproof · cited by 13
- FractionalIdeal.mul_defstatement and proof · cited by 6
- FractionalIdeal.map_mulproof · cited by 0