+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Algebra +--{: .hide} [[!include higher algebra - contents]] =-- #### (0,1)-Category theory +--{: .hide} [[!include (0,1)-category theory - contents]] =-- =-- =-- \tableofcontents ## Disambiguation Traditionally, in [[classical mathematics]], an ordered ring is a [[totally ordered ring]]. However, in [[constructive mathematics]], due to the failure of [[excluded middle]], there are multiple notions of order which are not necessarily equivalent to the notion of total order but which in the presence of [[excluded middle]] are equivalent to the notion of [[total order]], and thus, there are multiple notions of ordered rings. There are also more general notions of ordered rings, where the order is a [[preorder]], a [[partial order]], a [[lattice]], a [[pseudo-order]], or a [[strict preorder]]. * [[preordered ring]] * [[totally preordered ring]] * [[prelattice-ordered ring]] * [[strictly weakly ordered ring]] * [[partially ordered ring]] * [[totally ordered ring]] * [[lattice-ordered ring]] * [[pseudo-ordered ring]] ## External links * Wikipedia, _<a href="https://en.wikipedia.org/wiki/Ordered_ring">Ordered ring</a>_ category: disambiguation