Completely 0-Simple and Linear Semigroups
Jan Okniński · 2020
In this chapter, the authors establish some basic notation, and they recall the definitions and fundamental results of the theory of semigroups required in the sequel. The class of 0-simple semigroups contains an important subclass of completely 0-simple semigroups. A trivial semigroup also will be included in the class of completely 0-simple semigroups. Let S be a 0-simple semigroup. Principal factors of a given semigroup S are used to study the properties of S through its “local” structure. This motivates the following classical definition. S is called semisimple if all its principal factors are 0-simple, and S is called completely semisimple if all its principal factors are completely 0-simple.