He initially worked on semigroup theory, and Rees factor semigroup is named after him.

The concept of Rees factor semigroup was introduced by David Rees in 1940.

The new semigroup obtained in this way is called the Rees factor semigroup of S modulo I and is denoted by S/I.

In mathematics, in semigroup theory, a Rees factor semigroup (also called Rees quotient semigroup or just Rees factor) is a certain semigroup constructed using a semigroup and an ideal of the semigroup.

A semigroup S is called an ideal extension of a semigroup A by a semigroup B if A is an ideal of S and the Rees factor semigroup S/A is isomorphic to B.