High Quality Content by WIKIPEDIA articles! 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. Let S be a semigroup and I be an ideal of S. Using S and I one can construct a new semigroup by collapsing I into a single element while the elements of S outside of I retain their identity. The new semigroup obtained in this way is called the Rees factor semigroup of S modulo I and is denoted by S/I. The concept of Rees factor semigroup was introduced by D Rees in 1940.

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