Theorems · Theorem · commutative algebra
IsIntegral.isAlmostIntegral_of_exists_smul_mem_range
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {s : S},
IsIntegral R s → (∃ t ∈ nonZeroDivisors R, t • s ∈ (algebraMap R S).range) → IsAlmostIntegral R s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites44
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
- Finset.sumproof · cited by 5,195
- Algebra.algebraMapstatement and proof · cited by 4,706
- Submonoidstatement · cited by 3,086
- Finset.sum_congrproof · cited by 2,323
- LT.lt.leproof · cited by 2,189
- SMulCommClassproof · cited by 1,927
- one_smulproof · cited by 1,374
- Finset.rangeproof · cited by 1,341
- Polynomial.natDegreeproof · cited by 1,105
Cited by1
Results whose statement or proof uses this declaration.
- IsIntegral.isAlmostIntegral_of_isLocalizationproof · cited by 1