Semi-group - Encyclopedia of Mathematics
A set with one binary operation satisfying the law of associativity.A semi-group is a generalization of the concept of a group: only one of the group axioms is retained — associativity; this is the explanation of the term "semi-group" .Semi-groups are called monoids if they have, in addition, an identity element.. The theory of semi-groups is one of the relatively young branches of algebra.