hasIdentityElement
P19411
predicate
Indicates that a binary operation on a set has a special element which, when combined with any element of the set, leaves that element unchanged.
All labels observed (7)
| Label | Occurrences |
|---|---|
| identityElement | 18 |
| hasIdentityElement canonical | 17 |
| hasAdditiveIdentity | 2 |
| hasNeutralElement | 2 |
| givesMonoidStructureTo | 1 |
| hasMultiplicativeIdentity | 1 |
| multiplicativeIdentity | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: hasIdentityElement
Generated description
Indicates that a binary operation on a set has a special element which, when combined with any element of the set, leaves that element unchanged.
Sample triples (42)
| Subject | Object |
|---|---|
| Minkowski sum | set containing only the zero vector ⓘ |
|
Abelian group
linked to:
Abelian groups
|
0 in additive notation ⓘ |
|
Abelian group
linked to:
Abelian groups
|
e in multiplicative notation ⓘ |
| Euclidean group | identity isometry via predicate surface "identityElement" ⓘ |
| E(n) | identity isometry of R^n ⓘ |
| Dawg Pound | dog masks via predicate surface "identityElement" ⓘ |
| Dawg Pound | dog bone props via predicate surface "identityElement" ⓘ |
| Dawg Pound | brown and orange team colors via predicate surface "identityElement" ⓘ |
| Lie ring | 0 via predicate surface "hasAdditiveIdentity" ⓘ |
|
SO(3)
linked to:
rotation group SO(3)
|
3×3 identity matrix via predicate surface "identityElement" ⓘ |
| Whitney sum | zero vector bundle ⓘ |
| Whitney sum | set of isomorphism classes of vector bundles over a base space via predicate surface "givesMonoidStructureTo" ⓘ |
| Hadamard product (of power series) | power series with all coefficients equal to 1 via predicate surface "identityElement" ⓘ |
| Dirichlet convolution | true ⓘ |
| Dirichlet convolution | delta function at 1 via predicate surface "identityElement" ⓘ |
| The Thundering Herd | symbol of community resilience in Huntington, West Virginia via predicate surface "identityElement" ⓘ |
| Gator Nation | school spirit via predicate surface "identityElement" ⓘ |
| Gator Nation | athletic pride via predicate surface "identityElement" ⓘ |
| Gator Nation | alumni loyalty via predicate surface "identityElement" ⓘ |
| Gator Nation | campus traditions via predicate surface "identityElement" ⓘ |
| orthogonal group O(n) | identity matrix I_n ⓘ |
| affine group of R^n | x ↦ x ⓘ |
|
SO(n)
linked to:
special orthogonal group SO(n)
|
n×n identity matrix via predicate surface "identityElement" ⓘ |
| U(1) | 1 ⓘ |
|
GL(n,ℝ)
linked to:
general linear group GL(n,R)
|
I_n ⓘ |
|
GL(n,ℝ)
linked to:
general linear group GL(n,R)
|
I_n via predicate surface "hasNeutralElement" ⓘ |
|
SL(n,ℝ)
linked to:
special linear group SL(n,R)
|
I_n ⓘ |
|
GL(n,ℂ)
linked to:
general linear group GL(n,C)
|
n×n identity matrix via predicate surface "identityElement" ⓘ |
|
SL(n,ℂ)
linked to:
special linear group SL(n,C)
|
identity matrix Iₙ ⓘ |
| Mordell curve | point at infinity ⓘ |
| GF(p) | 1 via predicate surface "multiplicativeIdentity" ⓘ |
| GF(p^m) | true via predicate surface "hasMultiplicativeIdentity" ⓘ |
| GF(p^m) | true via predicate surface "hasAdditiveIdentity" ⓘ |
| Griess algebra | yes ⓘ |
| SL(2,ℤ) | 2×2 identity matrix via predicate surface "identityElement" ⓘ |
| SL(2,R) | 2×2 identity matrix via predicate surface "identityElement" ⓘ |
| Witt group of quadratic forms | class of hyperbolic quadratic forms ⓘ |
| Witt group of quadratic forms | class of zero form in the Witt group ⓘ |
| Brauer group | class of the base field as a central simple algebra via predicate surface "identityElement" ⓘ |
| Twisted Edwards curve | (0,1) via predicate surface "hasNeutralElement" ⓘ |
| Picard group | class of the trivial line bundle O_X via predicate surface "identityElement" ⓘ |
| Mooloos | rural farming culture ⓘ |