nLab ordered ring

Context

Algebra

(0,1)-Category theory

Contents

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 pseudolattice, or a strict order.

category: disambiguation

Last revised on December 7, 2022 at 17:34:16. See the history of this page for a list of all contributions to it.