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 $x,y\in S$.

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 $\theta \in S$ such that $xy=\theta$ for all $x,y\in S$.

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