Statements (34)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:automorphismGroup |
gptkb:Weyl_group
|
| gptkbp:characteristic |
zero or a prime number
|
| gptkbp:defines |
a set with two operations (addition and multiplication) satisfying field axioms
|
| gptkbp:example |
complex numbers (C)
finite fields (Galois fields) rational numbers (Q) real numbers (R) |
| gptkbp:fileExtension |
finite field
|
| gptkbp:hasAxiom |
distributivity of multiplication over addition
|
| gptkbp:hasInverseOperation |
additive inverse
multiplicative inverse (except zero) |
| gptkbp:hasNeutralElement |
additive identity (zero)
multiplicative identity (one) |
| gptkbp:hasSubgroup |
ring (algebra)
commutative ring with unity |
| https://www.w3.org/2000/01/rdf-schema#label |
fields (algebra)
|
| gptkbp:isCommutative |
addition
multiplication |
| gptkbp:namedAfter |
field (Feld) in German, introduced by Richard Dedekind
|
| gptkbp:notableFor |
every nonzero element has a multiplicative inverse
basis for vector spaces fundamental in algebraic structures no zero divisors |
| gptkbp:operator |
addition
multiplication |
| gptkbp:studiedIn |
abstract algebra
|
| gptkbp:subunit |
subfield
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
coding theory cryptography number theory |
| gptkbp:bfsParent |
gptkb:matrix_algebra_over_a_field
|
| gptkbp:bfsLayer |
8
|