nLab
protoring

Contents

Contents

Definition

A protoring is a commutative monoid (M,0,+)(M, 0, +) with a strict linear order <\lt such that

  • a<ba \lt b if and only if a+c<b+ca + c \lt b + c.

  • The commutative subsemigroup of strictly positive elements M +{xM|0<x}M_+ \coloneqq \{x \in M \vert 0 \lt x\} form a semiring (M,+,1,)(M, +, 1, \cdot).

  • a<ba \lt b if and only if ac<bca \cdot c \lt b \cdot c and ca<cbc \cdot a \lt c \cdot b.

Examples

See also

 References

  • Davorin Lešnik, Synthetic Topology and Constructive Metric Spaces, (arxiv:2104.10399)

Created on May 12, 2022 at 08:04:36. See the history of this page for a list of all contributions to it.