Theorems · Theorem · commutative algebra
IsIntegral.fg_adjoin_singleton
∀ {R : Type u_1} {B : Type u_3} [inst : CommRing R] [inst_1 : Ring B] [inst_2 : Algebra R B] {x : B},
IsIntegral R x → (Subalgebra.toSubmodule R[x]).FG- Cited by
- 13 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Subalgebrastatement · cited by 1,353
- Finset.rangeproof · cited by 1,341
- Polynomial.natDegreeproof · cited by 1,105
- Finset.imageproof · cited by 910
Cited by13
Results whose statement or proof uses this declaration.
- isIntegral_transproof · cited by 15
- IsIntegral.smulproof · cited by 13
- IsIntegral.powproof · cited by 12
- fg_adjoin_of_finiteproof · cited by 9
- RingHom.IsIntegralElem.of_mem_closureproof · cited by 4
- IsIntegral.negproof · cited by 4
- IsIntegral.invproof · cited by 2
- IsIntegral.inv_mem_adjoinproof · cited by 2
- IsIntegral.isUnitproof · cited by 1
- mem_integralClosure_iff_mem_fgproof · cited by 1
- Algebra.finite_adjoin_simple_of_isIntegralproof · cited by 1
- FractionalIdeal.isFractional_adjoin_integralproof · cited by 0