Theorems · Theorem · commutative algebra
IsLocalization.isInteger_smul
∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_2} [inst_1 : CommSemiring S] [inst_2 : Algebra R S] {a : R}
{b : S}, IsLocalization.IsInteger R b → IsLocalization.IsInteger R (a • b)- Defined in
- Mathlib.RingTheory.Localization.Integer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Algebra.algebraMapproof · cited by 4,706
- Algebra.smul_defproof · cited by 287
- RingHom.map_mulproof · cited by 45
- IsLocalization.IsIntegerstatement and proof · cited by 39
Cited by2
Results whose statement or proof uses this declaration.
- FractionalIdeal.isFractional_span_iffproof · cited by 2
- IsFractional.supproof · cited by 0