Category
page 1Ordered groups
Archimedean property
the absence of infinitesimals in a mathematical system
ordered field
field together with a total ordering of its elements such that the set of positive elements is translation-invariant and multiplicatively closed

ordered ring
ring with a compatible total order

ordered group
group with a compatible partial order
linearly ordered group
group with translationally invariant total order
ordered vector space
vector space with a partial order
Riesz space
partially ordered vector space, ordered as a lattice
formally real field
field that can be equipped with an ordering