nLab prevector space

Redirected from "prevector spaces".
Contents

Context

Algebra

Linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Constructivism, Realizability, Computability

Contents

Idea

In the same vein that commutative rings are to integral domains and GCD rings are to GCD domains, prevector spaces are to vector spaces.

Definition

A RR-module VV is a prevector space if RR is a prefield ring. The elements of VV are called vectors.

Examples

  • Every \mathbb{Q}-vector space is a \mathbb{Q}-prevector space.

  • Every classical vector space is a FF-prevector space for a classical field FF (defined using denial inequality).

  • Every Heyting vector space is a FF-prevector space for a Heyting field FF.

  • Every discrete vector space is a FF-prevector space for a discrete field FF.

  • Every residue vector space is a FF-prevector space for a residue field FF.

See also

Last revised on December 8, 2022 at 02:45:08. See the history of this page for a list of all contributions to it.