Theorems · Theorem · commutative algebra
IsLocalRing.of_isUnit_or_isUnit_of_isUnit_add
∀ {R : Type u_1} [inst : Semiring R] [Nontrivial R], (∀ (a b : R), IsUnit (a + b) → IsUnit a ∨ IsUnit b) → IsLocalRing R- Defined in
- Mathlib.RingTheory.LocalRing.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- SemiringNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Nontrivialstatement and proof · cited by 2,416
- IsUnitstatement and proof · cited by 1,602
- IsLocalRingstatement · cited by 339
- isUnit_oneproof · cited by 48
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalRing.of_surjectiveproof · cited by 1