Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

16Kxx Division rings and simple Artinian rings

This subtopic studies division rings and simple Artinian rings, exploring the structure of skew fields and related semisimple objects.

Specific topics

16K20 Finite-dimensional division rings

Overview

16K20 studies finite-dimensional division rings in division rings and simple artinian rings. It focuses on division rings, central simple algebras, and the Brauer-theoretic invariants that classify them.

Related Wikipedia Page

Finite-dimensional division rings (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for finite-dimensional division rings
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in the study of skew fields, central simple algebras, and equivalence classes of division algebra structures.

Applications

  • Division ring structure theory
  • Central simple algebra classification
  • Brauer groups and splitting fields

References

Recommended Textbooks

16K40 Infinite-dimensional and general division rings

Overview

16K40 studies infinite-dimensional and general division rings in division rings and simple artinian rings. It focuses on division rings, central simple algebras, and the Brauer-theoretic invariants that classify them.

Related Wikipedia Page

Infinite-dimensional and general division rings (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for infinite-dimensional and general division rings
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in the study of skew fields, central simple algebras, and equivalence classes of division algebra structures.

Applications

  • Division ring structure theory
  • Central simple algebra classification
  • Brauer groups and splitting fields

References

Recommended Textbooks

16K50 Brauer groups

Overview

16K50 studies brauer groups in division rings and simple artinian rings. It focuses on division rings, central simple algebras, and the Brauer-theoretic invariants that classify them.

Related Wikipedia Page

Brauer groups (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for brauer groups
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in the study of skew fields, central simple algebras, and equivalence classes of division algebra structures.

Applications

  • Division ring structure theory
  • Central simple algebra classification
  • Brauer groups and splitting fields

References

Recommended Textbooks