null semigroup
A left zero semigroup is a semigroup in which every element is a left zero element. In other words, it is a set S with a product defined as xy=x for all x,y∈S.
A right zero semigroup is defined similarly.
Let S be a semigroup. Then S is a null semigroup if it has a zero element and if the product of any two elements is zero. In other words, there is an element θ∈S such that xy=θ for all x,y∈S.
| Title | null semigroup |
|---|---|
| Canonical name | NullSemigroup |
| Date of creation | 2013-03-22 13:02:22 |
| Last modified on | 2013-03-22 13:02:22 |
| Owner | mclase (549) |
| Last modified by | mclase (549) |
| Numerical id | 4 |
| Author | mclase (549) |
| Entry type | Definition |
| Classification | msc 20M99 |
| Related topic | Semigroup |
| Related topic | ZeroElements |
| Defines | null semigroup |
| Defines | left zero semigroup |
| Defines | right zero semigroup |