Completely Weak Simple Semigroups and Weak 0-simple Semigroups

The structure theorems for simple semigroups and -simple semigroups has proved a very powerful tools in the investigation of such semigroups. In this paper first of all we define weak simple semigroups and weak -simple semigroups. Also define natural partial order relation on idempotents of semigroup. Then we define completely weak simple semigroup and completely weak -simple semigroup, and by using Green's equivalences, we prove some results and give equivalences, for this semigroups

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Green