Definition:Totally Ordered Semigroup

Definition
A totally ordered semigroup is a totally ordered structure $\left({S, \circ, \preceq}\right)$ such that $\left({S, \circ}\right)$ is a semigroup.

Also see

 * Definition:Totally Ordered Structure


 * Definition:Naturally Ordered Semigroup
 * Definition:Positively Totally Ordered Semigroup
 * Definition:Right Naturally Totally Ordered Semigroup
 * Definition:Left Naturally Totally Ordered Semigroup
 * Definition:Naturally Totally Ordered Semigroup