Null semigroup
SEMIGROUP WITH AN ABSORBING ELEMENT, CALLED ZERO, IN WHICH THE PRODUCT OF ANY TWO ELEMENTS IS ZERO
Zero semigroup; Left zero semigroup; Right zero semigroup
In mathematics, a null semigroup (also called a zero semigroup) is a semigroup with an absorbing element, called zero, in which the product of any two elements is zero. If every element of a semigroup is a left zero then the semigroup is called a left zero semigroup; a right zero semigroup is defined analogously.