Theorems · Theorem · commutative algebra
IsLocalRing.isUnit_or_isUnit_of_isUnit_add
∀ {R : Type u_1} [inst : Semiring R] [IsLocalRing R] {a b : R}, IsUnit (a + b) → IsUnit a ∨ IsUnit b- Defined in
- Mathlib.RingTheory.LocalRing.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext
- Assumes
- SemiringIsLocalRing
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.
- Semiringstatement and proof · cited by 13,802
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- mul_addproof · cited by 413
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.isUnit_or_isUnit_of_add_oneproof · cited by 5
- Units.isUnit_units_mulproof · cited by 4
- Units.inv_mul_eq_oneproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- IsLocalRing.isUnit_or_isUnit_one_sub_selfproof · cited by 3
- AlgebraicGeometry.Scheme.basicOpen_add_leproof · cited by 1
- IsLocalRing.of_surjectiveproof · cited by 1
- IsLocalRing.nonunits_addproof · cited by 0