Theorems · Definition · order theory

MulArchimedeanClass.subsemigroup

{M : Type u_1} →
  [inst : CommGroup M] →
    [inst_1 : LinearOrder M] → [inst_2 : IsOrderedMonoid M] → UpperSet (MulArchimedeanClass M) → Subsemigroup M

Given a UpperSet of MulArchimedeanClass, all group elements belonging to these classes form a subsemigroup. This is not yet a subgroup because it doesn't contain the identity if s = ⊤.

Defined in

Mathlib.Algebra.Order.Archimedean.Class

Cited by

5 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupLinearOrderIsOrderedMonoid