Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:alsoKnownAs |
gptkb:von_Neumann_regular_ring
|
| gptkbp:category |
ring theory
|
| gptkbp:compatibleWith |
not all regular rings are commutative
|
| gptkbp:defines |
a ring in which every element a has an x such that a = axa
|
| gptkbp:example |
any field
the product of fields the ring of n x n matrices over a division ring |
| gptkbp:field |
abstract algebra
|
| gptkbp:generalizes |
gptkb:Boolean_ring
division ring |
| https://www.w3.org/2000/01/rdf-schema#label |
regular ring
|
| gptkbp:introducedIn |
1936
|
| gptkbp:namedAfter |
gptkb:John_von_Neumann
|
| gptkbp:property |
every principal left ideal is generated by an idempotent
every principal right ideal is generated by an idempotent |
| gptkbp:relatedTo |
semisimple ring
idempotent element |
| gptkbp:bfsParent |
gptkb:Cohen–Macaulay_ring
gptkb:Gorenstein_ring gptkb:von_Neumann_regular_ring |
| gptkbp:bfsLayer |
6
|