Theorems · Theorem · ring theory
QuadraticAlgebra.star_mem_nonZeroDivisors
∀ {R : Type u_2} {a b : R} [inst : CommRing R] {z : QuadraticAlgebra R a b},
z ∈ nonZeroDivisors (QuadraticAlgebra R a b) → star z ∈ nonZeroDivisors (QuadraticAlgebra R a b)- Defined in
- Mathlib.Algebra.QuadraticAlgebra.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Submonoidstatement · cited by 3,086
- mul_commproof · cited by 2,262
- Star.starstatement and proof · cited by 1,082
- nonZeroDivisorsstatement and proof · cited by 895
- QuadraticAlgebrastatement and proof · cited by 123
- StarMul.star_mulproof · cited by 72
- star_zeroproof · cited by 58
- Function.Involutive.injectiveproof · cited by 26
- InvolutiveStar.star_involutiveproof · cited by 11
- mem_nonZeroDivisors_iff_rightproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- QuadraticAlgebra.norm_mem_nonZeroDivisors_iffproof · cited by 0
- QuadraticAlgebra.star_mem_nonZeroDivisors_iffproof · cited by 0