Theorems · Theorem · ring theory
QuadraticAlgebra.rank_eq_two
∀ {R : Type u_1} (a b : R) [inst : Semiring R] [StrongRankCondition R], Module.rank R (QuadraticAlgebra R a b) = 2- Defined in
- Mathlib.Algebra.QuadraticAlgebra.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringStrongRankCondition
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Cardinalstatement · cited by 2,598
- Module.rankstatement · cited by 496
- StrongRankConditionstatement and proof · cited by 286
- Fintype.card_finproof · cited by 270
- QuadraticAlgebrastatement · cited by 123
- rank_eq_card_basisproof · cited by 8
- QuadraticAlgebra.basisproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- QuadraticAlgebra.finrank_eq_twoproof · cited by 0