Theorems · Theorem · commutative algebra
Ring.ord_ne_top
∀ {R : Type u_1} [inst : CommRing R] [IsNoetherianRing R] [Ring.KrullDimLE 1 R] {a : R},
a ∈ nonZeroDivisors R → Ring.ord R a ≠ ⊤- Cited by
- 3 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Top.topstatement · cited by 9,680
- ENatstatement · cited by 4,985
- Submonoidstatement · cited by 3,086
- nonZeroDivisorsstatement and proof · cited by 895
- IsNoetherianRingstatement and proof · cited by 268
- Ring.KrullDimLEstatement and proof · cited by 79
- Ring.ordstatement · cited by 28
- isFiniteLength_quotient_span_singletonproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Ring.ord_lt_topproof · cited by 1
- Ring.ordFrac_ge_one_of_ne_zeroproof · cited by 1
- Ring.ordMonoidHom_eq_ordproof · cited by 0