Theorems · Definition · commutative algebra
Units.posSubgroup
(R : Type u_1) → [inst : Semiring R] → [inst_1 : LinearOrder R] → [IsStrictOrderedRing R] → Subgroup Rˣ
The subgroup of positive units of a linear ordered semiring.
- Defined in
- Mathlib.Algebra.Ring.Subring.Units
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredproof · cited by 6,101
- Subgroupstatement · cited by 3,593
- Submonoidproof · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Units.valproof · cited by 1,966
- Submonoid.comapproof · cited by 179
- Units.coeHomproof · cited by 44
- Submonoid.posproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.GLPosproof · cited by 16
- Units.mem_posSubgroupstatement · cited by 0
- Units.index_posSubgroupstatement and proof · cited by 0
- sameRay_of_mem_orbitstatement and proof · cited by 0
- Units.posSubgroup.congr_simpstatement and proof · cited by 0