Theorems · Theorem · commutative algebra
FractionalIdeal.isFractional_adjoin_integral
∀ {R : Type u_1} [inst : CommRing R] (S : Submonoid R) {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
[IsLocalization S P] (x : P), IsIntegral R x → IsFractional S (Subalgebra.toSubmodule R[x])A[x] is a fractional ideal for every integral x.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- 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
- Subalgebrastatement · cited by 1,353
- IsLocalizationstatement and proof · cited by 636
- OrderEmbeddingstatement · cited by 619
- Algebra.adjoinstatement · cited by 535
- IsIntegralstatement and proof · cited by 427
- Subalgebra.toSubmodulestatement · cited by 141
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.adjoinIntegralproof · cited by 4