Theorems · Theorem · ring theory
QuadraticAlgebra.norm_mem_nonZeroDivisors_iff
∀ {R : Type u_2} {a b : R} [inst : CommRing R] {z : QuadraticAlgebra R a b},
QuadraticAlgebra.norm z ∈ nonZeroDivisors R ↔ z ∈ nonZeroDivisors (QuadraticAlgebra R a b)- Defined in
- Mathlib.Algebra.QuadraticAlgebra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- MonoidHomstatement · cited by 3,629
- Submonoidstatement · cited by 3,086
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- Star.starproof · cited by 1,082
- nonZeroDivisorsstatement and proof · cited by 895
- QuadraticAlgebrastatement and proof · cited by 123
- QuadraticAlgebra.improof · cited by 44
- QuadraticAlgebra.reproof · cited by 43
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