Field theory and polynomials Basic notions Concept
Division ring
Summary
A division ring is a nonzero ring in which every nonzero element has a multiplicative inverse. It is like a field, but the multiplication need not be commutative. The definition of a division ring gives the conditions.
Where this leads
24 pages build on this one.
- Unit-regular ring
- Semifield
- Quaternionic analysis
- Near-field
- Finite Desarguesian planes are Pappian
- Maximal subfield
- Amitsur's noncrossed product
- Kaplansky's theorem on PI rings
- Artinian reduced rings are semisimple
- Kurosh problem
- von Neumann regular ring
- Jacobson density theorem
- Quasifield
- Posner's theorem
- Period and index
- Goldie's theorem
- Schur's lemma in abelian categories
- Veblen–Young theorem
- Levitzki's theorem
- Lenagan's theorem
- Artin–Wedderburn theorem
- Endomorphism ring of a simple module is a division ring
- Hopkins–Levitzki theorem
- Wedderburn's theorem on simple Artinian rings
Further reading
- Web https://en.wikipedia.org/wiki/Division_ring, lead section
About this page
| Tag | 0EA5BTA0CX |
|---|---|
| URI | m2://0EA5BTA0CX |
| Aliases | skew-field |
| Kind | concept |
| Writing | W1 stated |
| MSC | 12E15 |
| Specializes | Ring |
| Same as |
Markdown · JSON · Edit on GitHub
What this page needs for W2
- edge instance_of in: at least two examples (1 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Special cases
Instances
Definitions
Used by
- Semifield
- Quaternionic analysis
- Near-field
- Finite Desarguesian planes are Pappian
- Maximal subfield
- Amitsur's noncrossed product
- Kaplansky's theorem on PI rings
- Artinian reduced rings are semisimple
- Kurosh problem
- von Neumann regular ring
- Quasifield
- Period and index
- Schur's lemma in abelian categories
- Veblen–Young theorem
- Artin–Wedderburn theorem
- Endomorphism ring of a simple module is a division ring
- Wedderburn's theorem on simple Artinian rings