Theorems · Definition · commutative algebra
IsLocalRing.nonunitsAddSubmonoid
(R : Type u_1) → [inst : Semiring R] → [IsLocalRing R] → AddSubmonoid R
The nonunits of a local semiring form an additive submonoid.
- Defined in
- Mathlib.RingTheory.LocalRing.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext
- Assumes
- SemiringIsLocalRing
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
- AddSubmonoidstatement · cited by 1,178
- IsLocalRingstatement and proof · cited by 339
- nonunitsproof · cited by 35
- IsLocalRing.nonunits_addproof · cited by 0
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalRing.maximalIdealproof · cited by 297
- IsLocalRing.exists_of_isUnit_sumproof · cited by 0