Example · Undergraduate
Terms
| Term | This example | Why |
|---|
| module |
✓ |
The pairs of integers $\mathbb{Z}^2$, with addition and multiplication by integers, form a module over the ring $\mathbb{Z}$, because the rules of a vector space hold with integer scalars.
|
| vector space |
✗ |
The pairs of integers $\mathbb{Z}^2$, with multiplication by integers, do not form a vector space, because the integers do not form a field.
|
| algebra (over a field) |
✗ |
The pairs of integers $\mathbb{Z}^2$, with addition and multiplication by integers, do not form an algebra over a field, because the scalars do not form a field and no multiplication of two pairs is given.
|
Distinctions using this example
All examples · All distinctions · All definitions