Theorems · Theorem · commutative algebra
PowerBasis.adjoin_gen_eq_top
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] (B : PowerBasis R S),
R[B.gen] = ⊤- Defined in
- Mathlib.RingTheory.PowerBasis
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Top.topstatement · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Submoduleproof · cited by 7,192
- Set.rangeproof · cited by 4,705
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement and proof · cited by 535
- eq_top_iffproof · cited by 236
Cited by4
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.adjoin_singleton_eq_topproof · cited by 3
- Module.Basis.traceDual_powerBasis_eqproof · cited by 1
- PowerBasis.adjoin_eq_top_of_gen_mem_adjoinproof · cited by 0
- conductor_eq_top_of_powerBasisproof · cited by 0